FOR IMMEDIATE RELEASE                                 Contact: Greg Wright
                                                          (210)283-2440




                       TESORO COUNTERS DISSIDENT GROUP'S
                    LATEST CLAIMS IN LETTER TO STOCKHOLDERS


     San  Antonio,  Texas  --  March  15,  1996  -- Tesoro Petroleum Corporation
(NYSE:TSO) today said its Board of  Directors  is sending a letter to all Tesoro
shareholders, urging careful consideration  of  the  facts  before  acting  upon
materials  recently  mailed  to them by a dissident group led by Kevin Flannery.
The board  reiterated  its  recommendation  that  shareholders  support Tesoro's
current leadership and strategy, and to either not give consents or  revoke  any
consents given to the Flannery group.

     In  the letter, Tesoro President and Chief Executive Officer Bruce A. Smith
tells stockholders:  "Don't let the Flannery  Group mislead you into giving them
control of your investment.  Don't give them the keys to the company so they can
generate wealth for themselves!."

     The full text of Tesoro's letter follows.

     Tesoro  Petroleum  Corporation  is  a  natural  resource company engaged in
natural gas exploration and  production,  petroleum  refining and marketing, and
marine services.


                                 March 15, 1996






 Dear Fellow Shareholder:

 The Stockholders' Committee for New Management of Tesoro Petroleum  Corporation
 (the  "Flannery  Group")  JUST DOESN'T UNDERSTAND!  Recently, they wrote to you
 raising several issues to which we want to respond.

                  WHAT HAS HAPPENED TO THE VALUE OF OUR STOCK?

 While shareholder value is ultimately measured  by the increase in the price of
 Tesoro's stock, most investors understand that the drivers of value are  future
 earnings  and cash flow.  Since your board put this management team in place in
 1992, earnings and cash flow have increased each year to record levels in 1995.
 So why hasn't the stock price  increased?   It has, almost tripling since 1992.
 But what the Flannery Group fails to tell you, or understand, is  the  negative
 impact  that  the 1995 Tennessee Gas decision by the Texas Supreme Court had on
 our stock price.  We believe much  of  the  30%  decline they talk about can be
 linked to this adverse decision's expected effect  on  future  earnings.   They
 want  to  avoid  the issue because, in management's view, this litigation might
 have been settled were it  not  for Flannery's interference which led Tennessee
 Gas to suspend negotiations with the company and close a window of  opportunity
 to  settle the matter.  If they don't understand the fundamental effect of this
 issue on the stock (and  debt),  do  you  want  them  working for you to create
 shareholder value?

                      THE REFINING AND MARKETING BUSINESS

 The Flannery Group criticizes expenditures for Tesoro's refining and  marketing
 business.   In  earlier  communications,  the Group criticized the high-return,
 quick-payback vacuum unit, which has had  a  positive impact that resulted in a
 contribution  of  approximately  $14  million  in  1995.    Excluding   capital
 expenditures  related  to  the  vacuum  unit,  Tesoro  has  generated  positive
 operating  cash  flow  in  excess  of expenditures during the last three years.
 They also criticize the $90 million  of  debt attributed to the refinery.  This
 is another half-truth since two-thirds of that amount represents the settlement
 of a claim by the State of Alaska against the company  for  approximately  $100
 million   which  threatened  to  bankrupt  the  company  and  would  have  left
 shareholders with little or no value!




                               THE BOB WEST FIELD

 The Flannery Group provides more half-truths concerning the company's sale of a
 part of its Bob West  Field  interests.   First they criticized the sale.  Then
 they applauded the sale.  Now, they criticize the sale again because the  buyer
 announced  it  had  successfully  drilled  two  new  wells.  The Flannery Group
 doesn't understand  economics.   A  successful  well  doesn't  mean an adequate
 return on investment will be received by shareholders.  In fact, the sale looks
 even better today because the sold  properties  are  producing  below  what  we
 predicted  and new wells are not even being drilled as quickly as we predicted.
 Aggregate production from the sold properties is almost 25% below levels at the
 time we sold.  Do you really want the lack of understanding demonstrated by the
 Flannery Group to be applied to your investment in Tesoro?

                            A NEW BOARD OF DIRECTORS

 The Flannery Group criticizes the director retirement plan  which  many  public
 corporations  the  size of Tesoro have.  But he says it will potentially prompt
 "what will amount to a boardroom exodus."   Yet, he wants your consent to throw
 out the entire current board!  What does he really want?  Under the  governance
 guidelines adopted by your board, by the 1996 annual meeting, Tesoro's Board of
 Directors  is  expected  to  be comprised of two directors elected in 1996, one
 director named in 1995, three directors  named  in 1992, and one director named
 in 1983.  This is a new board!

          THE FLANNERY GROUP HAS NO CREDIBLE PLAN FOR TESORO PETROLEUM
                                  -- JUST TALK

   Their only recommendation for increasing shareholder value is:

     "The Alaskan Refining Business Should be Divested."
                         Original Mailing to Shareholders by Flannery Group

 Now,  after reading the company's materials, the Flannery Group has changed its
mind calling for

     "Disposition of the Refining Business at the appropriate time...."
                         Latest Mailing to Shareholders by Flannery Group

 The Flannery Group  has  finally  agreed  with  us  that  a refinery sale under
 current industry conditions destroys shareholder  value.   Tesoro's  management
 and  industry experts have said that selling a refinery now is a bad idea.  Our
 refining and marketing business  can  add  value  and  we have a strategy which
 focuses on higher margin products and expanding  our  marketing  efforts  while
 minimizing  future  capital  investment.  Good management finds ways to improve
 cash flow and earnings -- that increases shareholder value!




          THE FLANNERY GROUP ADMITS ITS "PLAN" MAY PRODUCE NO RESULTS
                                FOR SHAREHOLDERS

 They have stated in their mailing  that  "the trading price of the Common Stock
 is, of course, influenced by many factors and, therefore, it is  impossible  to
 say with certainty that its price will increase or to predict the amount of any
 such increase that might occur."

 It's  obvious  from 1995 results that management is having an impact on what is
 in its control, but the same external forces that have impacted the stock price
 under Tesoro's current management  would  undoubtedly  have a similar influence
 for the Flannery Group.

                            SEND THE GREEN CARD NOW

 Don't let the Flannery Group mislead you  into  giving  them  control  of  your
 investment.   Don't  give  them  the  keys  to the company so they can generate
 wealth for themselves!

 THE BOARD URGES YOU NOT TO SUPPORT  THE FLANNERY GROUP IN ITS ATTEMPT TO REMOVE
 AND REPLACE YOUR BOARD OF DIRECTORS AND URGES YOU TO REVOKE ANY  WHITE  CONSENT
 CARD THAT MAY HAVE BEEN GIVEN.

 If you have previously returned a white consent card, you have every  right  to
 change  your  mind and revoke your consent by signing, dating and returning the
 accompanying GREEN revocation of consent  card, using the enclosed postage-paid
 envelope.  Even if you have not previously signed or returned a  white  consent
 card  to  the  Flannery  Group,  you  may sign and return a GREEN revocation of
 consent card to Tesoro, which will have  no legal effect but would assist us in
 monitoring the progress of the Flannery Group's consent solicitation.

                              Thank you for your support,


                              /s/ Bruce A. Smith

                              Bruce A. Smith
                              President and Chief Executive Officer

                    If your shares of Common Stock are held
                    in the name of a bank or brokerage firm,
       only that firm can execute a revocation of consent on your behalf.

        Please contact the person responsible for your account and give
              instructions for a GREEN revocation of consent card
                   to be voted REVOKING CONSENT on all items.

     If you have questions or need assistance in voting your shares, please
         contact the firm assisting us in the solicitation of proxies:

                            GEORGESON & COMPANY INC.
                           TOLL FREE: 1-800-223-2064
                       BANKS & BROKERS CALL: 212-440-9800

               INTERNET: World Wide Web http://www.georgeson.com