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                         NOTICE OF GUARANTEED DELIVERY
 
                   FOR 9% SENIOR SUBORDINATED NOTES DUE 2008
                        OF TESORO PETROLEUM CORPORATION
 
     As set forth in the Prospectus dated           , 1998 (the "Prospectus") of
Tesoro Petroleum Corporation, a Delaware corporation (the "Company"), and in the
Letter of Transmittal (the "Letter of Transmittal"), this form or a form
substantially equivalent to this form must be used to accept the Exchange Offer
(as defined below) if the certificates for the outstanding 9% Senior
Subordinated Notes due 2008 (the "Old Notes") of the Company and all other
documents required by the Letter of Transmittal cannot be delivered to the
Exchange Agent by the expiration of the Exchange Offer or compliance with
book-entry transfer procedures cannot be effected on a timely basis. Such form
may be delivered by hand or transmitted by facsimile transmission, telex or mail
to the Exchange Agent no later than the Expiration Date, and must include a
signature guarantee by an Eligible Institution as set forth below. Capitalized
terms used herein but not defined herein have the meanings ascribed thereto in
the Prospectus.
 
        TO: U.S. BANK TRUST NATIONAL ASSOCIATION (THE "EXCHANGE AGENT")
 

                                                          
 By Registered, Certified, or               By Hand                  By First Class Mail:
  Overnight Mail or Courier:
     U.S. Bank Trust N.A.            U.S. Bank Trust N.A.            U.S. Bank Trust N.A.
   Attn: Specialized Finance      4th Floor Bond Drop Window            P.O. Box 64485
           SPFT0414                  180 East Fifth Street          St. Paul, MN 55164-9549
     180 East Fifth Street            St. Paul, MN 55101
      St. Paul, MN 55101
                                         By Facsimile:
                                  (For Eligible Institutions
                                            Only):
                                        (651) 244-1537

 
     DELIVERY OF THIS INSTRUMENT TO AN ADDRESS OTHER THAN AS SET FORTH ABOVE
DOES NOT CONSTITUTE A VALID DELIVERY. THE METHOD OF DELIVERY OF ALL DOCUMENTS,
INCLUDING CERTIFICATES, IS AT THE RISK OF THE HOLDER. IF DELIVERY IS BY MAIL,
REGISTERED OR CERTIFIED MAIL WITH RETURN RECEIPT REQUESTED, PROPERLY INSURED, IS
RECOMMENDED. THE INSTRUCTIONS ACCOMPANYING THE LETTER OF TRANSMITTAL SHOULD BE
READ CAREFULLY BEFORE THIS NOTICE OF GUARANTEED DELIVERY IS COMPLETED.
 
     This Notice of Guaranteed Delivery is not to be used to guarantee
signatures. If a signature on a Letter of Transmittal is required to be
guaranteed by an Eligible Institution under the instruction thereto, such
signatures must appear in the applicable space provided on the Letter of
Transmittal for Guarantee of Signature(s).
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Ladies and Gentlemen:
 
     The undersigned acknowledges receipt of the Prospectus and the related
Letter of Transmittal which describes the Company's offer (the "Exchange Offer")
to exchange $1,000 in principal amount of a new series of 9% Senior Subordinated
Notes due 2008, Series B (the "Exchange Notes") for each $1,000 in principal
amount of the Old Notes.
 
     The undersigned hereby tenders to the Company the aggregate principal
amount of Old Notes set forth below on the terms and conditions set forth in the
Prospectus and the related Letter of Transmittal pursuant to the guaranteed
delivery procedure set forth in the "The Exchange Offer -- Guaranteed Delivery
Procedures" section in the Prospectus and the accompanying Letter of
Transmittal.
 
     The undersigned understands that no withdrawal of a tender of Old Notes may
be made after the Expiration Date. The undersigned understands that for a
withdrawal of a tender of Old Notes to be effective, a written notice of
withdrawal that complies with the requirements of the Exchange Offer must be
timely received by the Exchange Agent at one of its addresses specified on the
cover of this Notice of Guaranteed Delivery prior to the Expiration Date.
 
     The undersigned understands that the exchange of Old Notes for Exchange
Notes pursuant to the Exchange Offer will be made only after timely receipt by
the Exchange Agent of (i) such Old Notes (or Book-Entry Confirmation of the
transfer of such Old Notes into the Exchange Agent's account at The Depository
Trust Company (the "Depositary" or "DTC")) and (ii) a Letter of Transmittal (or
facsimile thereof) with respect to such Old Notes, properly completed and duly
executed, with any required signature guarantees, this Notice of Guaranteed
Delivery and any other documents required by the Letter of Transmittal or a
properly transmitted Agent's Message. The term "Agent's Message" means a message
transmitted by the Depositary to, and received by, the Exchange Agent and
forming part of the confirmation of a book-entry transfer, which states that the
Depositary has received an express acknowledgment from each participant in the
Depositary tendering the Old Notes and that such participant has received the
Letter of Transmittal and agrees to be bound by the terms of the Letter of
Transmittal and the Company may enforce such agreement against such participant.
 
     All authority conferred or agreed to be conferred by this Notice of
Guaranteed Delivery shall not be affected by, and shall survive, the death or
incapacity of the undersigned, and every obligation of the undersigned under
this Notice of Guaranteed Delivery shall be binding upon the heirs, executors,
administrators, trustees in bankruptcy, personal and legal representatives,
successors and assigns of the undersigned.
 
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                            PLEASE SIGN AND COMPLETE
 
Signature(s) of Registered Owner(s) or Authorized Name(s) of Registered
Holder(s)
 

                                                
 
Signatory:                                         --------------------------------------------
- ------------------------------------------         --------------------------------------------
- --------------------------------------------       --------------------------------------------
- --------------------------------------------       Address:
Principal Amount of Old Notes Tendered:            --------------------------------------------
- --------------------------------------------       --------------------------------------------
Certificate No.(s) of Old Notes (if                Area Code and Telephone No.:
available):                                        -------------------
- --------------------------------------------       If Old Notes will be delivered by book-entry
- --------------------------------------------       transfer at The Depository Trust Company,
Date:                                              insert
- --------------------------------------------       Depository Account No.:
                                                   --------------------------

 
This Notice of Guaranteed Delivery must be signed by the registered Holder(s) of
Old Notes exactly as its (their) name(s) appears on certificates for Old Notes
or on a security position listing as the owner of Old Notes, or by person(s)
authorized to become registered Holder(s) by endorsements an documents
transmitted with this Notice of Guaranteed Delivery. If signature is by a
trustee, executor, administrator, guardian, attorney-in-fact, officer or other
person acting in a fiduciary or representative capacity, such person must
provide the following information.
 
                      PLEASE PRINT NAME(S) AND ADDRESS(ES)
 
Name(s):    --------------------------------------------------------------------
            --------------------------------------------------------------------
 
            --------------------------------------------------------------------
 
Capacity:   --------------------------------------------------------------------
 
Address(es):--------------------------------------------------------------------
            --------------------------------------------------------------------
 
            --------------------------------------------------------------------
 
DO NOT SEND OLD NOTES WITH THIS FORM. OLD NOTES SHOULD BE SENT TO THE EXCHANGE
AGENT TOGETHER WITH A PROPERLY COMPLETED AND DULY EXECUTED LETTER OF
TRANSMITTAL.
 
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                                   GUARANTEE
                    (NOT TO BE USED FOR SIGNATURE GUARANTEE)
 
     The undersigned, a member firm of a registered national securities exchange
or of the National Association of Securities Dealers, Inc. or a commercial bank
or trust company having an office or a correspondent in the United States, or
otherwise an "eligible guarantor institution" within the meaning of Rule 17Ad-15
under the Securities Exchange Act of 1934, as amended, hereby (a) represents
that each holder of Old Notes on whose behalf this tender is being made "own(s)"
the Old Notes covered hereby within the meaning of Rule l3d-3 under the
Securities Exchange Act of 1934, as amended (the "Exchange Act") and (b)
guarantees that, within three New York Stock Exchange trading days from the
expiration date of the Exchange Offer, a properly completed and duly executed
Letter of Transmittal (or a facsimile thereof), together with certificates
representing the Old Notes covered hereby in proper form for transfer (or
confirmation of the book-entry transfer of such Old Notes into the Exchange
Agent's account at The Depository Trust Company, pursuant to the procedure for
book-entry transfer set forth in the Prospectus) and required documents will be
deposited by the undersigned with the Exchange Agent.
 
     The undersigned acknowledges that it must deliver the Letter of Transmittal
and Old Notes tendered hereby to the Exchange Agent within the time period set
forth above and that failure to do so could result in financial loss to the
undersigned.
 

                                                
 
Name of Firm:                                      --------------------------------------------
- -------------------------------------              Authorized Signature
Address:                                           Name:
- --------------------------------------------       --------------------------------------------
- --------------------------------------------       Title:
Area Code and Telephone No.:                       --------------------------------------------
- -------------------                                Date:
                                                   --------------------------------------------

 
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