1
                                                                     EXHIBIT 4.1




                           CERTIFICATE OF DESIGNATION
                                       OF
                  7.25% MANDATORILY CONVERTIBLE PREFERRED STOCK
                                       OF
                          TESORO PETROLEUM CORPORATION

                                  -------------

               Pursuant to Section 151 of the General Corporation
                          Law of the State of Delaware

                                  -------------

                  TESORO PETROLEUM CORPORATION, a corporation organized and
existing under the General Corporation Law of the State of Delaware (the
"Company"), does hereby certify that the following resolution was duly adopted
by the Board of Directors of the Company (the "Board") at a special meeting of
the Board of Directors held on June 23, 1998:


                  RESOLVED, that pursuant to the authority conferred upon the
Board by the provisions of the Company's Restated Certificate of Incorporation
(the "Certificate") and in accordance with Section 151 of the General
Corporation Law of the State of Delaware, the Board hereby creates, from the
5,000,000 shares of preferred stock, no par value per share (the "Preferred
Stock"), of the Company, authorized to be issued pursuant to the Certificate, a
series of Preferred Stock consisting of 103,500 shares of 7.25% Mandatorily
Convertible Preferred Stock and hereby fixes the voting powers, designations,
preferences and relative, participating, optional or other special rights, and
qualifications, limitations or restrictions of such preferences and/or rights,
of the shares of that series as follows:

                  Section 1. Designation. (a) The shares of the series will be 
designated as the 7.25% Mandatorily Convertible Preferred Stock (the
"Mandatorily Convertible Preferred Stock"). The total number of authorized
shares of the Mandatorily Convertible Preferred Stock will be 103,500.

                  (b) Any shares of the Mandatorily Convertible Preferred Stock
that at any time have been acquired upon conversion or otherwise acquired by the
Company shall, after such conversion or other acquisition, resume the status of
authorized and unissued shares of Preferred Stock without designation as to
series until such shares are once more designated as part of a particular series
by the Board.

                  Section 2. Rank.

                  The shares of Mandatorily Convertible Preferred Stock will
rank on parity, both as to payment of dividends and distribution of assets upon
liquidation, with any Preferred Stock issued by the Company in the future that
by its terms ranks pari passu with the shares of Mandatorily Convertible
Preferred Stock.

                  Section 3. Dividends. (a) The holders of record of the shares 
of Mandatorily Convertible Preferred Stock shall be entitled to receive, when,
as and if declared by the Board out of funds legally available therefor, cash
dividends ("Preferred



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Dividends") from the date of the initial issuance of the shares of Mandatorily
Convertible Preferred Stock at the rate of 7.25% per annum or 1.8125% per
quarter per share of Mandatorily Convertible Preferred Stock, payable quarterly
in arrears on January 1, April 1, July 1 and October 1 or, if any such date is
not a business day (as defined in Section 7 hereof), the Preferred Dividend due
on such date shall be payable on the next succeeding business day (each such
payment date being a "Regular Dividend Payment Date"), subject to upward
adjustment pursuant to Section 3(c) hereof. The first dividend period will be
from the date of initial issuance of the shares of Mandatorily Convertible
Preferred Stock to but excluding October 1, 1998 and will be payable on October
1, 1998. Preferred Dividends shall cease to accrue on shares of Mandatorily
Convertible Preferred Stock on the Mandatory Conversion Date (as defined in
Section 4 hereof) or on the date of their earlier conversion. Preferred
Dividends shall be payable to holders of record of shares of Mandatorily
Convertible Preferred Stock as they appear on the stock register of the Company
on record dates not less than 15 nor more than 60 days preceding the payment
date thereof, as shall be fixed by the Board. Preferred Dividends payable on
shares of Mandatorily Convertible Preferred Stock for any period less than a
full quarterly dividend period (or, in the case of the first Preferred Dividend,
from the date of initial issuance of the shares of Mandatorily Convertible
Preferred Stock to the first Regular Dividend Payment Date) will be computed on
the basis of a 360-day year of twelve 30-day months and the actual number of
days elapsed in any period less than one month. Preferred Dividends shall accrue
on a daily basis (computed as set forth in the immediately preceding sentence)
whether or not there are funds of the Company legally available for the payment
of such Preferred Dividends and whether or not such Preferred Dividends are
declared. Accrued but unpaid Preferred Dividends shall cumulate as of the
Regular Dividend Payment Date on which they first become payable, but no
interest shall accrue on accumulated but unpaid Preferred Dividends.

                  (b)  Whether or not the Mandatory Conversion Date has 
occurred,

                  (i) no dividends (other than dividends payable in shares of,
         or warrants, rights or options exercisable for or convertible into
         shares of, any capital stock, including without limitation, the Common
         Stock, of the Company ranking junior to the Mandatorily Convertible
         Preferred Stock as to the payment of dividends and the distribution of
         assets upon liquidation (collectively "Junior Stock") and cash in lieu
         of fractional shares in connection with any such dividend) may be paid
         or declared in cash or otherwise, nor may any other distribution by
         made (other than a distribution payable in Junior Stock and cash in
         lieu of fractional shares in connection with any such distribution), on
         any Junior Stock;

                  (ii) no shares of any Junior Stock may be purchased, redeemed
         or otherwise acquired by the Company or any of its subsidiaries (except
         in connection with a reclassification or exchange of any Junior Stock
         through the issuance of other Junior Stock (and cash in lieu of
         fractional shares in connection therewith) or the purchase, redemption
         or other acquisition of any Junior Stock with any Junior Stock (and
         cash in lieu of fractional shares in connection therewith)) nor may any
         funds be set aside or made available for any sinking funds for the
         purchase, redemption or acquisition of any Junior Stock; and

                  (iii) no dividends or other distributions may be declared or
         paid on any Preferred Stock (including the Mandatorily Convertible
         Preferred Stock) that does not constitute Junior Stock ("Parity
         Preferred Stock") (other than dividends



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         or other distributions payable in Junior Stock and cash in lieu of
         fractional shares in connection therewith), and the Company may not
         purchase, redeem or otherwise acquire any Parity Preferred Stock
         (except with any Junior Stock and cash in lieu of fractional shares in
         connection therewith and except with the right, subject to the
         requirement set out following clause (D) of this paragraph and any
         similar requirement of any other Preferred Stock, to receive accrued
         and unpaid dividends)

unless, in the case of either (i) or (ii) or (iii):

                  (A) full dividends on Parity Preferred Stock have been paid,
         or declared and set aside for payment, for all dividend periods
         terminating on or prior to the date of such dividend, distribution,
         purchase, redemption, acquisition, setting aside or making available,
         as applicable, to the extent such dividends are cumulative,

                  (B) dividends in full for the current quarterly dividend
         period have been paid, or declared and set aside for payment, on all
         Parity Preferred Stock to the extent such dividends are cumulative,

                  (C) the Company has paid or set aside all amounts, if any,
         then or theretofore required to be paid or set aside for all purchase,
         retirement and sinking funds, if any, for any Parity Preferred Stock,
         and

                  (D) the Company is not in default on any of its obligations to
         redeem any Parity Preferred Stock,

or, in the case of (iii) only, with respect to the declaration and payment of
dividends on Parity Preferred Stock, any such dividends are declared and paid
pro rata so that the amounts of any dividends declared and paid per share of
Mandatorily Convertible Preferred Stock and each other share of Parity Preferred
Stock will in all cases bear to each other the same ratio that accrued and
unpaid dividends (including any accumulation with respect to unpaid dividends
for prior dividend periods, if such dividends are cumulative) per share of
Mandatorily Convertible Preferred Stock and such other share of Parity Preferred
Stock bear to each other.

                  (c) If a Reset Transaction (as defined below) has occurred,
the dividend rate on the Mandatorily Convertible Preferred Stock shall be
increased (but not decreased) to the rate per annum that is the arithmetic
average of the rates quoted by two Reference Dealers (as defined in Section 7
hereof) selected by the Company or its successor as the dividend rate that the
Mandatorily Convertible Preferred Stock should bear so that the fair market
value, expressed in dollars, of a share of Mandatorily Convertible Preferred
Stock immediately after the later of (i) the public announcement of such Reset
Transaction and (ii) the public announcement of a change in dividend policy in
connection with such Reset Transaction but without giving effect to any
adjustments pursuant to Sections 4(e)(i) through 4(e)(iv) hereof, shall equal
the average Closing Price of a share of Mandatorily Convertible Preferred Stock
(it being understood that, in the event any shares of Mandatorily Convertible
Preferred Stock are represented by depositary shares, the average Closing Price
of the Mandatorily Convertible Preferred Stock shall be determined by reference
to the average Closing Price of such depositary shares) for the twenty Trading
Days immediately preceding the date of public



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announcement of such Reset Transaction. A "Reset Transaction" is any
consolidation, merger, sale, transfer or statutory exchange to which the
provisions of Section 4(f) apply or any dividend or distribution to which the
provisions of Section 4(e)(iv) apply, as a result of which the Mandatorily
Convertible Preferred Stock is convertible on and after the effective date of
such transaction into shares (including those of the Company) which either (i)
had a Dividend Yield (as defined in Section 7 hereof) for the four fiscal
quarters immediately preceding the public announcement of such transaction which
was, or (ii) are issued by an entity (including the Company) that has publicly
announced a dividend policy prior to the effective date of such transaction
which policy, if implemented, would result in a Dividend Yield on such shares
for the next four fiscal quarters which would be, more than 250 basis points
higher than the Dividend Yield on the Common Stock for the four fiscal quarters
immediately preceding the public announcement of such transaction.

                  (d) Whenever the dividend rate on the Mandatorily Convertible
Preferred Stock is increased as provided in Section 3(c), the Company or its
successor shall:

                  (i) forthwith compute the increased dividend rate in
         accordance with Section 3(c) and prepare a certificate signed by the
         Chief Financial Officer, any Vice President, the Treasurer or the
         Controller of the Company or its successor setting forth the increased
         dividend rate, the applicable rates quoted by the two Reference Dealers
         selected by the Company or its successor for such rate quotes and the
         arithmetic average of those rate quotes, and the facts requiring such
         increase and upon which such increase is based, which certificate shall
         be conclusive, final and binding evidence of the correctness of the
         increase, and shall file such certificate forthwith with the transfer
         agent or agents for the shares of Mandatorily Convertible Preferred
         Stock and any depositary for any shares of Mandatorily Convertible
         Preferred Stock represented by depositary shares;

                  (ii) make a prompt public announcement stating that the
         dividend rate on the Mandatorily Convertible Preferred Stock has been
         increased and setting forth the increased dividend rate; and

                 (iii) mail a notice stating that the dividend rate on the
         Mandatorily Convertible Preferred Stock has been increased, the facts
         requiring such increase and upon which such increase is based and
         setting forth the increased dividend rate to the holders of record of
         the outstanding shares of the Mandatorily Convertible Preferred Stock,
         and, in the event any shares of Mandatorily Convertible Preferred Stock
         are represented by depositary shares, to the holders of record of the
         depositary receipts evidencing such depositary shares, no later than 45
         days after the end of the Company's fiscal quarter period during which
         the Reset Transaction resulting in such increase occurred.

                  Section 4. Conversion Rights. (a) Unless previously converted
at the option of the holder into Common Stock in accordance with the provisions
of Section 4(c), on July 1, 2001 (the "Mandatory Conversion Date") each
outstanding share of Mandatorily Convertible Preferred Stock will convert
automatically (the "Mandatory Conversion") into a number of shares of Common
Stock at the Conversion Rate (as defined below) in effect on the Mandatory
Conversion Date and the holder thereof shall have the right to receive an amount
in cash equal to all accrued and unpaid Preferred Dividends on such share of
Mandatorily Convertible Preferred Stock (other than



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previously declared Preferred Dividends payable to a holder of record as of a
prior date) to the Mandatory Conversion Date, whether or not declared, out of
funds legally available for the payment of Preferred Dividends, subject to the
requirement set forth following clause (D) of Section 3(b) above and any similar
requirement of any other Certificate of Designations for Preferred Stock. The
"Conversion Rate" is initially equal to (i) if the Conversion Price (as defined
in Section 7 hereof) is greater than or equal to $18.85 (the "Threshold
Appreciation Price"), 84.55 shares of Common Stock per share of Mandatorily
Convertible Preferred Stock, (ii) if the Conversion Price is less than the
Threshold Appreciation Price but is greater than $15.9375 (the "Initial Price"),
(A) a fraction equal to the Initial Price divided by the Conversion Price of (B)
100 shares of Common Stock per share of Mandatorily Convertible Preferred Stock
and (iii) if the Conversion Price is less than or equal to the Initial Price,
100 shares of Common Stock per share of Mandatorily Convertible Preferred Stock.
The ratios of shares of Common Stock per share of Mandatorily Convertible
Preferred Stock specified in clauses (i), (ii) and (iii) of the immediately
preceding sentence are hereinafter referred to as the "Share Components". The
Share Components are subject to adjustment as set forth in Section 4(e) and the
Threshold Appreciation Price and the Initial Price are subject to adjustment as
set forth in Section 4(g).

                  (b) Preferred Dividends on the shares of Mandatorily
Convertible Preferred Stock shall cease to accrue and such shares of Mandatorily
Convertible Preferred Stock shall cease to be outstanding on the Mandatory
Conversion Date. The Company shall make such arrangements as it deems
appropriate for the issuance of certificates representing shares of Common Stock
and for the payment of cash in respect of accrued and unpaid dividends on the
Mandatorily Convertible Preferred Stock, if any, or cash in lieu of fractional
shares, if any, without interest, in exchange for and contingent upon surrender
of certificates representing the shares of Mandatorily Convertible Preferred
Stock, and the Company may defer the payment of dividends on such shares of
Common Stock until, and make such payment contingent upon, the surrender of
certificates representing the shares of Mandatorily Convertible Preferred Stock,
provided that the Company shall give the holders of the shares of Mandatorily
Convertible Preferred Stock such notice of any such actions as the Company deems
appropriate and upon such surrender such holders shall be entitled to receive
such dividends declared and paid, if any, without interest, on such shares of
Common Stock subsequent to the Mandatory Conversion Date.

                  (c) Shares of Mandatorily Convertible Preferred Stock are
convertible, in whole or in part, at the option of the holders thereof
("Optional Conversion"), at any time after July 26, 1998 and prior to the
Mandatory Conversion Date, into shares of Common Stock at a rate of 84.55 shares
of Common Stock for each share of Mandatorily Convertible Preferred Stock (the
"Optional Conversion Rate"), subject to adjustment as set forth in Sections 4(e)
and 4(f). Optional Conversion of shares of Mandatorily Convertible Preferred
Stock may be effected by delivering certificates evidencing such shares,
together with written notice of conversion and proper assignment of such
certificates to the Company or in blank (and, if Optional Conversion is to occur
after the close of business on a record date for any payment of declared
Preferred Dividends and before the opening of business on the next succeeding
dividend payment date, payment in cash of an amount equal to the Preferred
Dividend payable on such date on such shares), to the office of any transfer
agent for the shares of Mandatorily Convertible Preferred Stock or to any other
office or agency maintained by the Company for that purpose and otherwise in
accordance with Optional Conversion procedures established



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by the Company. Each Optional Conversion shall be deemed to have been effected
immediately prior to the close of business on the date on which the foregoing
requirements shall have been satisfied. The Optional Conversion shall be at the
Optional Conversion Rate in effect at such time on such date.

                  (d) Holders of shares of Mandatorily Convertible Preferred
Stock at the close of business on a record date for any payment of declared
Preferred Dividends shall be entitled to receive the Preferred Dividend so
declared on such shares of Mandatorily Convertible Preferred Stock on the
corresponding dividend payment date notwithstanding the Optional Conversion of
such shares of Mandatorily Convertible Preferred Stock following such record
date and prior to such dividend payment date. However, shares of Mandatorily
Convertible Preferred Stock surrendered for Optional Conversion after the close
of business on a record date for any payment of declared Preferred Dividends and
before the opening of business on the next succeeding dividend payment date must
be accompanied by payment in cash of an amount equal to the Preferred Dividend
payable on such date on such shares. Except as provided above, upon any Optional
Conversion of shares of Mandatorily Convertible Preferred Stock, the Company
shall make no payment of or allowance for unpaid Preferred Dividends, whether or
not in arrears, on such shares of Mandatorily Convertible Preferred Stock as to
which Optional Conversion has been effected or previously declared dividends or
distributions on the shares of Common Stock issued upon such Optional
Conversion.

                  (e) The Conversion Rate and the Optional Conversion Rate are
each subject to adjustment from time to time as provided below in this Section
4(e).

                  (i) If the Company shall pay or make a dividend or other
         distribution with respect to its Common Stock in shares of Common Stock
         (including by way of reclassification of any shares of its Common Stock
         (other than pursuant to any of the transactions set forth in Section
         4(f)), each of the Share Components and the Optional Conversion Rate in
         effect at the opening of business on the day following the date fixed
         for the determination of stockholders entitled to receive such dividend
         or other distribution shall be increased by multiplying each Share
         Component and the Optional Conversion Rate by a fraction of which the
         numerator shall be the sum of the number of shares of Common Stock
         outstanding at the close of business on the date fixed for such
         determination, excluding the effect of such dividend or distribution,
         plus the total number of shares of Common Stock constituting such
         dividend or other distribution, and of which the denominator shall be
         the number of shares of Common Stock outstanding at the close of
         business on the date fixed for such determination, excluding the effect
         of such dividend or distribution, such increase to become effective at
         the opening of business on the day following the date fixed for such
         determination. For the purposes of this Section 4(e)(i), the number of
         shares of Common Stock at any time outstanding shall not include shares
         held in the treasury of the Company and the number of shares
         constituting such dividend or other distribution shall include shares
         represented by cash issued in lieu of fractional shares of Common
         Stock.

                 (ii) In case shares of Common Stock outstanding shall be
         subdivided or split into a greater number of shares of Common Stock,
         each of the Share Components and the Optional Conversion Rate in effect
         at the opening of business on the day following the day upon which such
         subdivision or split



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         becomes effective shall be proportionately increased, and, conversely,
         in case outstanding shares of Common Stock shall be combined into a
         lesser number of shares of Common Stock, each of the Share Components
         and the Optional Conversion Rate in effect at the opening of business
         on the day following the day upon which such combination becomes
         effective shall be proportionately reduced, such increases or
         reductions, as the case may be, to become effective at the opening of
         business on the day following the day upon which such subdivision or
         split or combination becomes effective.

                 (iii) If the Company shall, after the date hereof, issue
         rights or warrants to all holders of its Common Stock entitling them to
         subscribe for or purchase shares of Common Stock at a price per share
         less than the Current Market Price (as defined in Section 7 hereof) of
         the Common Stock on the record date for the determination of
         stockholders entitled to receive such rights or warrants, then in each
         case each of the Share Components and the Optional Conversion Rate
         shall be adjusted by multiplying such Share Components and the Optional
         Conversion Rate in effect on such record date by a fraction of which
         the numerator shall be the number of shares of Common Stock outstanding
         at the close of business on the record date for issuance of such rights
         or warrants, excluding the effect of such issuance, plus the number of
         additional shares of Common Stock offered for subscription or purchase
         pursuant to such rights or warrants, and of which the denominator shall
         be the number of shares of Common Stock outstanding at the close of
         business on the record date for issuance of such rights or warrants,
         excluding the effect of such issuance, plus the number of shares of
         Common Stock which the aggregate offering price of the total number of
         shares of Common Stock so offered for subscription or purchase pursuant
         to such rights or warrants would purchase at such Current Market Price
         (determined by multiplying such total number of offered shares by the
         exercise price of such rights or warrants and dividing the product so
         obtained by such Current Market Price). Such adjustment shall become
         effective at the opening of business on the business day next following
         the record date for the determination of stockholders entitled to
         receive such rights or warrants. Shares of Common Stock held by the
         Company or by another company of which a majority of the shares
         entitled to vote in the election of directors are held, directly or
         indirectly, by the Company shall not be deemed to be outstanding for
         purposes of such computation. Any shares of Common Stock issuable in
         payment of a dividend shall be deemed to have been issued immediately
         prior to the close of business on the record date for such dividend for
         purposes of calculating the number of outstanding shares of Common
         Stock under this Section 4(e)(iii). To the extent that shares of Common
         Stock are not delivered by reason of the expiration of such rights or
         warrants, each of the Share Components and the Optional Conversion Rate
         shall be readjusted to the Share Components and the Optional Conversion
         Rate which would then be in effect had the adjustments made by reason
         of the issuance of such rights or warrants been made upon the basis of
         the issuance of rights or warrants in respect of only the number of
         shares of Common Stock actually delivered.

                  (iv) If the Company shall pay a dividend or make a
         distribution to all holders of Common Stock consisting of evidences of
         its indebtedness, cash or other assets (including shares of capital
         stock of the Company other than dividends or distributions of Common
         Stock (or other common stock of the



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         Company issued by way of reclassification) referred to in Section
         4(e)(i) above but excluding any cash dividends or distributions, other
         than Extraordinary Cash Distributions (as defined below)), or shall
         issue to all holders of Common Stock rights or warrants to subscribe
         for or purchase any of its securities (other than those referred to in
         Section 4(e)(iii) above), then in each such case each of the Share
         Components and the Optional Conversion Rate shall be adjusted by
         multiplying such Share Components and the Optional Conversion Rate in
         effect on the record date for such dividend or distribution or for the
         determination of stockholders entitled to receive such rights or
         warrants, as the case may be, by a fraction of which the numerator
         shall be the Current Market Price per share of the Common Stock on such
         record date, and of which the denominator shall be such Current Market
         Price per share of Common Stock less either (A) the fair market value
         (as determined by the Board, whose determination shall be conclusive)
         on such record date of the portion of the assets or evidences of
         indebtedness so distributed, or of such rights or warrants, applicable
         to one share of Common Stock or (B) if applicable, the amount of the
         Extraordinary Cash Distribution applicable to one share of Common
         Stock. Such adjustment shall become effective at the opening of
         business on the business day next following the record date for such
         dividend or distribution or for the determination of holders entitled
         to receive such rights or warrants, as the case may be. "Extraordinary
         Cash Distribution" means, with respect to any cash dividend or
         distribution paid on any date, the amount, if any, by which all cash
         dividends or distributions on the Common Stock paid during the
         consecutive 12-month period ending on and including such date (other
         than cash dividends and cash distributions for which a prior adjustment
         to each of the Share Components and the Optional Conversion Rate was
         previously made), exceeds, on a per share of Common Stock basis, ten
         percent (10%) of the average daily Closing Price of the Common Stock
         over such consecutive 12-month period.

                  (v)   Anything in this Section 4 notwithstanding, the Company
         shall be entitled (but shall not be required) to make such upward
         adjustments in each of the Share Components and the Optional Conversion
         Rate in addition to those set forth by this Section 4, as the Company,
         in its sole discretion, shall determine to be advisable, in order that
         any stock dividend, subdivision or split of stock, distribution of
         rights to purchase stock or securities, or distribution of securities
         convertible into or exchangeable for stock (or any transaction that
         could be treated as any of the foregoing transactions pursuant to
         Section 305 of the Internal Revenue Code of 1986, as amended, or any
         successor provision) hereafter made by the Company to its stockholders
         will not be taxable in whole or in part.

                  (vi)  All adjustments to each of the Share Components and the
         Optional Conversion Rate shall be calculated to the nearest 1/100th of
         a share of Common Stock. No adjustment in the Share Components or the
         Optional Conversion Rate shall be required unless such adjustment would
         require an increase or decrease of at least one percent (1%) therein;
         provided, however, that any adjustments which are not made by reason of
         this subsection shall be carried forward and taken into account in any
         subsequent adjustment. All adjustments to the Share Components and the
         Optional Conversion Rate shall be made successively.

                  (vii) Prior to taking any action that could result in
         adjustment affecting the Conversion Rate or the Optional Conversion
         Rate such that the imputed



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         conversion price for shares of Common Stock issued upon Mandatory
         Conversion or upon Optional Conversion would be below the then par
         value of the Common Stock, the Company shall take any corporate action
         which may, in the opinion of its Board, be necessary in order that the
         Company may validly and legally issue fully paid and nonassessable
         shares of Common Stock at the Conversion Rate or the Optional
         Conversion Rate as so adjusted.

                  (f) In case of any consolidation or merger to which the
Company is a party (other than a merger or consolidation in which the Company is
the surviving or continuing corporation and in which each share of Common Stock
outstanding immediately prior to the merger or consolidation remains unchanged
in all material respects), or in case of any sale or transfer to another
corporation of the property of the Company as an entirety or substantially as an
entirety, or in the case of any statutory exchange of securities with another
corporation (other than in connection with a merger or acquisition), each share
of Mandatorily Convertible Preferred Stock shall, after consummation of such
transaction, be subject to (i) conversion at the option of the holder into the
kind and amount of securities, cash or other property receivable upon
consummation of such transaction by a holder of the number of shares of Common
Stock (including fractional shares for this purpose) into which such share of
Mandatorily Convertible Preferred Stock might have been converted immediately
prior to consummation of such transaction (or, if such transaction is
consummated prior to July 26, 1998, into which such share of Mandatorily
Convertible Preferred Stock might have been converted immediately prior to
consummation of such transaction if such conversion had occurred immediately
after such date) and (ii) conversion on the Mandatory Conversion Date into the
kind and amount of securities, cash or other property receivable upon
consummation of such transaction by a holder of the number of shares of Common
Stock (including fractional shares for this purpose) into which such share of
Mandatorily Convertible Preferred Stock would have been converted if the
conversion on the Mandatory Conversion Date had occurred immediately prior to
the date of consummation of such transaction, plus, in the case of (ii), the
right, subject to the requirement set forth following clause (D) of Section 3(b)
and any similar requirement of any other Certificate of Designations for
Preferred Stock, to receive cash in an amount equal to all accrued and unpaid
dividends on such share of Mandatorily Convertible Preferred Stock (other than
previously declared dividends payable to a holder of record as of a prior date);
and assuming in each case that such holder of shares of Common Stock failed to
exercise rights of election, if any, as to the kind or amount of securities,
cash or other property receivable upon consummation of such transaction
(provided that, if the kind or amount of securities, cash or other property
receivable upon consummation of such transaction is not the same for each
non-electing share, then the kind and amount of securities, cash or other
property receivable upon consummation of such transaction for each non-electing
share shall be deemed to be the kind and amount so receivable per share by a
plurality of the non-electing shares). The kind and amount of securities into or
for which the shares of Mandatorily Convertible Preferred Stock shall be
convertible after consummation of such transaction shall be subject to
adjustment as described in Section 4(e) following the date of consummation of
such transaction. The Company may not become a party to any such transaction
unless the terms thereof are consistent with the foregoing and with the
provisions of Section 3(c).

                  (g) If an adjustment is made to the Share Components pursuant
to any of Sections 4(e)(i) through 4(e)(iv), an adjustment shall also be made to
the Threshold Appreciation Price and the Initial Price as such terms are used to
determine which of



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clauses (i), (ii) or (iii) of the definition of "Conversion Rate" will apply at
the Mandatory Conversion Date and for purposes of calculating the fraction in
sub-clause (ii)(A) of the definition of Conversion Rate. The required
adjustments to the Threshold Appreciation Price and the Initial Price shall be
made at the Mandatory Conversion Date by multiplying each of the Threshold
Appreciation Price and the Initial Price by the inverse of the cumulative number
or fraction determined pursuant to the Share Component adjustment procedures
described in Section 4(e). In the case of the reclassification of any shares of
Common Stock into any common stock other than Common Stock, such common stock
shall be deemed Common Stock solely to determine the Threshold Appreciation
Price and the Initial Price and to apply the Conversion Rate at the Mandatory
Conversion Date. Each such adjustment to the Threshold Appreciation Price or the
Initial Price shall be made successively.

                  (h) Whenever the Share Components and the Optional Conversion
Rate are adjusted as provided in Section 4(e) and 4(g), the Company shall:

                  (i)   forthwith compute the adjusted Share Components, 
         Optional Conversion Rate, Threshold Appreciation Price and Initial
         Price in accordance with this Section 4 and prepare a certificate
         signed by the Chief Financial Officer, any Vice President, the
         Treasurer or the Controller of the Company setting forth the adjusted
         Share Components, Optional Conversion Rate, Threshold Appreciation
         Price and Initial Price, the method of calculation thereof in
         reasonable detail and the facts requiring such adjustment and upon
         which such adjustment is based, which certificate shall be conclusive,
         final and binding evidence of the correctness of the adjustment, and
         shall file such certificate forthwith with the transfer agent or agents
         for the shares of Mandatorily Convertible Preferred Stock and any
         depositary for any shares of Mandatorily Convertible Preferred Stock
         represented by depositary shares;

                  (ii)  make a prompt public announcement stating that the Share
         Components, Optional Conversion Rate, Threshold Appreciation Price and
         Initial Price have been adjusted and setting forth the adjusted Share
         Components, Optional Conversion Rate, Threshold Appreciation Price and
         Initial Price, including, in the event any shares of Mandatorily
         Convertible Preferred Stock are represented by depositary shares, the
         adjusted Share Components or Optional Conversion Rate on a per
         depositary share basis; and

                  (iii) mail a notice stating that the Share Components,
         Optional Conversion Rate, Threshold Appreciation Price and Initial
         Price have been adjusted, the facts requiring such adjustment and upon
         which such adjustment is based and setting forth the adjusted Share
         Components, Optional Conversion Rate, Threshold Appreciation Price and
         Initial Price to the holders of record of the outstanding shares of the
         Mandatorily Convertible Preferred Stock, and, in the event any shares
         of Mandatorily Convertible Preferred Stock are represented by
         depositary shares, to the holders of record of the depositary receipts
         evidencing such depositary shares, no later than 45 days after the end
         of the Company's fiscal quarter period during which the facts requiring
         such adjustment occurred.

                  (i)  In case, at any time while any of the shares of 
Mandatorily Convertible Preferred Stock are outstanding,




   11


                                                                              11

                  (i)   the Company shall declare a dividend (or any other
         distribution) on the Common Stock, excluding any cash dividends other
         than Extraordinary Cash Distributions, or

                  (ii)  the Company shall authorize the issuance to all holders
         of the Common Stock of rights or warrants to subscribe for or purchase
         shares of the Common Stock or of any other subscription rights or
         warrants, or

                  (iii) the Company shall authorize any reclassification of the
         Common Stock (other than a subdivision, split or combination thereof)
         or of any consolidation or merger to which the Company is a party and
         for which approval of any stockholders of the Company is required
         (except for a merger of the Company into one of its subsidiaries solely
         for the purpose of changing the corporate domicile of the Company to
         another state of the United States and in connection with which there
         is no substantive change in the rights or privileges of any securities
         of the Company other than changes resulting from differences in the
         corporate statutes of the state the Company was then domiciled in and
         the new state of domicile), or of the sale or transfer of all or
         substantially all the assets of the Company (except to one or more
         wholly owned subsidiaries),

then the Company shall cause to be filed at each office or agency maintained for
the purpose of conversion of the shares of Mandatorily Convertible Preferred
Stock, and shall cause to be mailed to the holders of shares of Mandatorily
Convertible Preferred Stock at their last addresses as they shall appear on the
stock register, and, in the event any shares of Mandatorily Convertible
Preferred Stock are represented by depositary shares, to the holders of record
of the depositary receipts evidencing such depositary shares, at least 10
business days before the date specified in clause (A) or (B) below (or the
earlier of such specified dates, in the event that more than one date is
specified), a notice stating (A) the date on which a record is to be taken for
the purpose of such dividend, distribution, or issuance of rights or warrants,
or, if a record is not to be taken, the date as of which the holders of Common
Stock of record to be entitled to such dividend, distribution, or issuance of
rights or warrants are to be determined, or (B) the date on which any such
reclassification, consolidation, merger, sale or transfer is expected to become
effective, and the date as of which it is expected that holders of Common Stock
of record shall be entitled to exchange their Common Stock for securities or
other property (including cash), if any, deliverable upon such reclassification,
consolidation, merger, sale or transfer. The failure to give or receive the
notice required by this subsection (i) or any defect therein shall not affect
the legality or validity of any such dividend, distribution, issuance of any
right or warrant or other action.

                  5. No Fractional Shares. (a) No fractional shares of Common
Stock shall be issued upon the conversion of any shares of the Mandatorily
Convertible Preferred Stock. In lieu of any fractional share otherwise issuable
in respect of shares of Mandatorily Convertible Preferred Stock of any holder
that are converted upon Mandatory Conversion or any Optional Conversion, such
holder shall be entitled to receive an amount in cash (computed to the nearest
cent) equal to the same fraction of the Closing Price of the Common Stock
determined (a) as of the fifth Trading Day immediately preceding the Mandatory
Conversion Date, in the case of Mandatory Conversion, or (b) as of the second
Trading Day immediately preceding the effective date of conversion, in the case
of an Optional Conversion by a holder. At any time that any shares of
Mandatorily Convertible Preferred Stock are represented by depositary



   12


                                                                              12

shares pursuant to a depositary agreement with the Company, the Company may
treat each holder of such depositary shares as a holder of the number (including
fractions) of shares of Mandatorily Convertible Preferred Stock represented by
the depositary shares of such holder for the purposes of computing the
fractional shares of Common Stock otherwise issuable in respect of the
conversion of any shares of Mandatorily Convertible Preferred Stock or the
payment of any dividend.

                  (b) If payment in cash in lieu of fractional shares of Common
Stock in accordance with the preceding paragraph would result in the Company's
failure to be in compliance with any debt instrument to which it is a party, the
Company shall be entitled to deliver a whole share of Common Stock in lieu of
cash to holders of shares of Mandatorily Convertible Preferred Stock (or
depositary shares representing shares of Mandatorily Convertible Preferred
Stock) entitled to fractional shares of Common Stock (beginning with the holders
entitled to the largest fractional shares) until delivery of cash in lieu of
fractional shares of Common Stock to the remaining holders would no longer
result in the Company's failure to be in compliance with such debt instrument.

                  6. Reservation of Common Stock. The Company shall at all times
reserve and keep available out of its authorized and unissued Common Stock,
solely for issuance upon the conversion of shares of Mandatorily Convertible
Preferred Stock as herein provided, free from any preemptive rights, such
maximum number of shares of Common Stock as shall from time to time be issuable
upon the Mandatory Conversion or Optional Conversion of all the shares of
Mandatorily Convertible Preferred Stock then outstanding.

                  7.  Certain Definitions. As used in this Certificate of 
Designations:

                  (i)   the term "business day" shall mean any day other than a
         Saturday, a Sunday or a day on which the NYSE, banking institutions or
         trust companies in New York, New York, are authorized or obligated by
         law or executive order to close;

                  (ii)  the term "Closing Price" of any security shall mean on
         any date of determination (i) the closing sale price (or, if no closing
         sale price is reported, the last reported sale price) of such security
         (regular way) on the New York Stock Exchange (the "NYSE") on such date,
         (ii) if such security is not listed for trading on the NYSE on any such
         date, as reported in the composite transactions for the principal
         United States securities exchange on which such security is so listed,
         (iii) if such security is not so listed on a United States securities
         exchange, as reported by the NASDAQ Stock Market, (iv) if such security
         is not so reported, the last quoted bid price for such security in the
         over-the-counter market as reported by the National Quotation Bureau or
         similar organization, or (v) if such security is not so quoted, the
         average of the mid-point of the last bid and ask prices for such
         security from each of at least three nationally recognized investment
         banking firms selected by the Company for such purpose;

                  (iii) the term "Conversion Price" shall mean the average
         Closing Price per share of Common Stock for the 20 Trading Days
         immediately prior to (but not including) the Mandatory Conversion Date;
         provided, however, that, if there are not 20 Trading Days for the
         Common Stock occurring later than the 60th calendar day immediately
         prior to, but not including, the Mandatory Conversion Date, the



   13


                                                                              13

         "Conversion Price" shall be the market value per share of Common Stock
         as of the Mandatory Conversion Date as determined by a nationally
         recognized investment banking firm retained for such purpose by the
         Company;

                  (iv)   the term "Current Market Price" means, as of any date
         of determination, the average Closing Price per share of Common Stock
         for the 20 Trading Days immediately prior to the date of determination;
         provided, however, that if there are not 20 Trading Days for the Common
         Stock occurring later than the 60th calendar day immediately prior to,
         but not including, such date, the Current Market Price shall be
         determined as the market value per share of Common Stock as of such
         date as determined by a nationally recognized investment banking firm
         retained for such purpose by the Company;

                  (v)    the term "Dividend Yield" shall mean, with respect to
         any security for any period, the dividends paid or proposed to be paid
         pursuant to an announced dividend policy on such security for such
         period divided by, if with respect to dividends paid on such security,
         the average Closing Price of such security during such period and, if
         with respect to dividends so proposed to be paid on such security, the
         Closing Price of such security on the effective date of the related
         Reset Transaction;

                  (vi)   the term "record date" shall be such date as is from 
         time to time fixed by the Board with respect to the receipt of
         dividends or the taking of any action or exercise of any voting rights
         permitted hereby; and

                  (vii)  the term "Reference Dealer" shall mean a dealer engaged
         in the trading of convertible securities;

                  (viii) the term "Trading Day" shall mean a business day on
         which the security, the Closing Price of which is being determined, (A)
         is not suspended from trading on any national or regional securities
         exchange or association or over-the-counter market at the close of
         business and (B) has traded at least once on the national or regional
         securities exchange or association or over-the-counter market that is
         the primary market for the trading of such security.

                  8. Payment of Taxes. The Company shall pay any and all
documentary, stamp or similar issue or transfer taxes payable in respect of the
issue or delivery of shares of Common Stock on the conversion of shares of
Mandatorily Convertible Preferred Stock pursuant to Section 4; provided,
however, that the Company shall not be required to pay any tax which may be
payable in respect of any registration or transfer involved in the issue or
delivery of shares of Common Stock in a name other than that of the registered
holder of shares of Mandatorily Convertible Preferred Stock converted or to be
converted, and no such issue or delivery shall be made unless and until the
person requesting such issue or delivery has paid to the Company the amount of
any such tax or has established, to the satisfaction of the Company, that such
tax has been paid.

                  9. Liquidation Rights. In the event of any voluntary or
involuntary liquidation, dissolution or winding up of the Company, and subject
to the rights of the holders of any other series of Preferred Stock, the holders
of outstanding shares of Mandatorily Convertible Preferred Stock are entitled to
receive the sum of $1,593.75 per share, plus an amount equal to any accrued and
unpaid dividends thereon, out of the



   14


                                                                              14

assets of the Company available for distribution to stockholders, before any
distribution of assets is made to holders of Junior Stock upon liquidation,
dissolution or winding up. If upon any voluntary or involuntary liquidation,
dissolution, or winding up of the Company, the assets of the Company are
insufficient to permit the payment of the full preferential amounts payable with
respect to shares of Mandatorily Convertible Preferred Stock and all other
series of Parity Preferred Stock, the holders of shares of Mandatorily
Convertible Preferred Stock and of all other series of Parity Preferred Stock
shall share ratably in any distribution of assets of the Company in proportion
to the full respective preferential amounts to which they are entitled. After
payment of the full amount of the liquidating distribution to which they are
entitled, the holders of shares of Mandatorily Convertible Preferred Stock will
not be entitled to any further participation in any distribution of assets by
the Company. A consolidation or merger of the Company with one or more
corporations or a sale or transfer of substantially all the assets of the
Company shall not be deemed to be a liquidation, dissolution, or winding up of
the Company.

                  10. Voting Rights. The holders of shares of Mandatorily
Convertible Preferred Stock shall not be entitled to any voting rights, except
as required by applicable state law or as described below.

                  (a) In the event that dividends on the shares of Mandatorily
Convertible Preferred Stock or any other series of Preferred Stock shall be in
arrears and unpaid for six quarterly dividend periods, or if any other series of
Preferred Stock shall be entitled for any other reason to exercise voting
rights, separate from the Common Stock, to elect any Directors of the Company
("Preferred Stock Directors"), the holders of the shares of Mandatorily
Convertible Preferred Stock (voting separately as a class with holders of all
other series of Preferred Stock which does not have a separate class vote and
upon which like voting rights have been conferred and are exercisable), with
each share of Mandatorily Convertible Preferred Stock entitled to 100 votes on
this and other matters in which Preferred Stock votes as a group, shall be
entitled to vote for the election of two Preferred Stock Directors, such
Directors to be in addition to the number of Directors constituting the Board
immediately prior to the accrual of such right. Such right, when vested, shall
continue until all dividends in arrears on the shares of Mandatorily Convertible
Preferred Stock and such other series of Preferred Stock shall have been paid in
full and the right of any other series of Preferred Stock to exercise voting
rights, separate from the Common Stock, to elect any Preferred Stock Directors
shall terminate or have terminated, and, when so paid and such termination
occurs or has occurred, such right of the holders of the shares of Mandatorily
Convertible Preferred Stock shall cease. Upon any termination of the aforesaid
voting right, subject to the requirements of the General Corporation Law of the
State of Delaware and the Certificate, such Preferred Stock Directors shall
cease to be Directors of the Company and shall be required to resign.

                  (b) The Company will not, without the approval of the holders
of at least 66-2/3% of all the shares of Mandatorily Convertible Preferred Stock
then outstanding: (i) amend, alter, or repeal any of the provisions of the
Certificate or the By-laws of the Company so as to affect adversely the powers,
preferences or rights of the holders of the shares of Mandatorily Convertible
Preferred Stock then outstanding or reduce the minimum time required for any
notice to which only the holders of the shares of Mandatorily Convertible
Preferred Stock then outstanding may be entitled (an amendment of the
Certificate to authorize or create, or to increase the authorized amount



   15


                                                                              15

of or to issue, Junior Stock, Preferred Stock ranking on parity with the shares
of Mandatorily Convertible Preferred Stock or any stock of any class ranking on
parity with the shares of Mandatorily Convertible Preferred Stock shall be
deemed not to affect adversely the powers, preferences or rights of the holders
of the shares of Mandatorily Convertible Preferred Stock); (ii) create any
series of Preferred Stock ranking prior to the shares of Mandatorily Convertible
Preferred Stock as to payment of dividends or the distribution of assets upon
liquidation; or (iii) authorize or create, or increase the authorized amount of,
any capital stock, or any security convertible into capital stock, of any class
ranking prior to the shares of Mandatorily Convertible Preferred Stock as to
payment of dividends or the distribution of assets upon liquidation.




   16


                                                                              16

                  11. Severability of Provisions. Whenever possible, each
provision hereof shall be interpreted in a manner as to be effective and valid
under applicable law, but if any provision hereof is held to be prohibited by or
invalid under applicable law, such provision shall be ineffective only to the
extent of such prohibition or invalidity, without invalidating or otherwise
adversely affecting the remaining provisions hereof. If a court of competent
jurisdiction should determine that a provision hereof would be valid or
enforceable if a period of time were extended or shortened or a particular
percentage were increased or decreased, then such court may make such change as
shall be necessary to render the provision in question effective and valid under
applicable law.


                  IN WITNESS WHEREOF, Tesoro Petroleum Corporation has caused
this Certificate of Designation to be signed by James C. Reed, Jr., its
Executive Vice President, General Counsel and Secretary, and attested by , its
Assistant Secretary, as of this 25th day of June, 1998.

                                        TESORO PETROLEUM CORPORATION,

                                        By /s/ BRUCE A. SMITH
                                           -------------------------------------
                                        Name:  Bruce A. Smith
                                        Title: Chairman, President, and Chief
                                                Executive Officer



Attest:

  By /s/ JAMES C. REED, JR.
     --------------------------
     Name:  James C. Reed, Jr.
     Title: Secretary