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




               TESORO SAYS DISSIDENT GROUP'S CONSENT SOLICITATION
                 IS BASED UPON MISCONCEPTIONS AND SELF-INTEREST
     Board Urges Shareholders to Support Management and Revoke Any Consents
                            Given to Dissident Group


     San Antonio,  Texas  --  March  6,  1996  --  Tesoro  Petroleum Corporation
(NYSE:TSO) today said its Board of Directors has sent a  letter  to  all  Tesoro
shareholders,  along  with  a  Revocation  of Consent Statement, as filed by the
company  with  the  Securities  and   Exchange  Commission.   The  letter  urges
shareholders  to  support  Tesoro's  current  management  and  board  and  their
strategy, and to either not give consents or revoke  any  consents  given  to  a
dissident group led by Kevin Flannery.

     In  the letter, Tesoro President and Chief Executive Officer Bruce A. Smith
states:  "The fruits  of  our  turnaround  strategy  are  becoming more and more
apparent and hold the potential to significantly  improve  future  performance."
The  letter  goes  on  to  outline the financial restructuring and the operating
strategy  at  Tesoro's  three   divisions   which   have,  since  1992  --  when
implementation of the strategy first began -- resulted in a tenfold increase  in
operating  profit,  a nearly tripled stock price and debt reduction of more than
$100 million.

     At the same time, the letter  states  that  "the arguments set forth by the
Flannery Group are seriously flawed and misleading and that the Flannery Group's
proposed  agenda  for  the  Company  is  totally  unrealistic,  is  based   upon
misconceptions  and  ignorance  of  Tesoro's  business  and our industry and has
little bearing on the real  choices  facing  Tesoro.  Worse, Mr. Flannery -- who
has already led two unsuccessful attempts to take over Tesoro -- appears  to  be
motivated by self-interest at the expense of the other Tesoro stockholders."

     The  letter  is  also  accompanied  by  a letter of support from Board Vice
Chairman  Steven  H.   Grapstein,   who   represents  Oakville,  N.V.,  Tesoro's
second-largest shareholder.  Oakville had  supported  prior  efforts  to  remove
certain  directors.   Grapstein  states  in  his  letter  that  the investors he
represents "are pleased  with  the  turnaround  that  has  been  underway at the
company, which has begun

                                     -more-

to  show  very  satisfying  results.   We believe that implementing management's
current strategy is the  best  one  for  Tesoro's  shareholders and will lead to
further improvements."

     Additionally,  Grapstein  states  in  his letter, "We are also pleased with
certain governance changes which have  recently  been implemented by the Board,"
and "we believe that  the  proposed  governance  policies,  director  succession
plans, management changes and current strategy are moving Tesoro on a path which
is in the best interest of all shareholders."

     In conclusion, he wrote, "As a result of all these positive developments at
the  company,  we  have decided to fully support Tesoro's management in opposing
the consent solicitation of the  dissident  group,"  and continues, "We ... urge
all shareholders who have supported the dissidents in the past  to  join  us  in
support of management in its efforts to continue with its current program."

     Full texts of Tesoro's and Grapstein's letters follow.

     Pursuant  to  the  rules  of  the  Securities  and Exchange Commission, the
following  sets  forth  certain  information  with  respect  to  the  beneficial
ownership of Common Stock  of  Tesoro  by  its  directors  as  of Feb. 24, 1996.

                                                          Shares
                                                          ------
Robert J. Caverly. . . . . . . . . . . . . . . . . . . . . .9,000  (1)
Peter M. Detwiler. . . . . . . . . . . . . . . . . . . . . 14,715  (1)
Steven H. Grapstein. . . . . . . . . . . . . . . . . . .1,528,900  (1)(2)
Raymond K. Mason, Sr.. . . . . . . . . . . . . . . . . . . 23,428  (1)
John J. McKetta, Jr. . . . . . . . . . . . . . . . . . . . .7,565  (1)
Bruce A. Smith . . . . . . . . . . . . . . . . . . . . . . 94,018  (3)
Murray L. Weidenbaum . . . . . . . . . . . . . . . . . . . .7,000  (1)

(1) The shares shown  for  Caverly,  Detwiler,  Grapstein,  Mason,  McKetta  and
    Weidenbaum  include  6,000 shares each which such directors had the right to
    acquire through the exercise of stock options on Feb. 24, 1996, or within 60
    days thereafter.

(2) The shares shown include 1,522,900  shares  of  Tesoro Common Stock owned by
    Oakville N.V. Grapstein is an  officer  of  Oakville  N.V.  As  an  officer,
    Grapstein shares voting and investment power with respect to such shares.

(3) The  shares  shown  include  1,304  shares credited to Smith's account under
    Tesoro's Thrift Plan and 80,866 shares  which Smith had the right to acquire
    through the exercise of stock options on Feb. 24, 1996, or  within  60  days
    thereafter.

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

                                      -30-

Bruce A. Smith
President and
Chief Executive Officer

                  PROTECT YOUR SHARE OF THE TESORO TURNAROUND!

                          DO NOT LET KEVIN FLANNERY'S
                        MISCONCEPTIONS AND SELF-INTEREST
                DEPRIVE YOU OF THE POTENTIAL OF YOUR INVESTMENT!

                     DO NOT RETURN ANY WHITE CONSENT CARDS!


                                                    March 4, 1996
Dear Fellow Shareholder:

     On January 30,  1996,  Tesoro  Petroleum  Corporation  announced  its  best
financial  performance  in over a decade.  This turnaround has been accomplished
by an  experienced  management  team  that  conceived  and  implemented a sound,
realistic strategy over the past three years.

     The turnaround and the potential value of your investment, however, are now
threatened.  A small group of shareholders, led by Kevin Flannery, is seeking to
seize control of your Company by soliciting consents to remove the current Board
and replace them with their hand-picked  nominees.   Your  Board  believes  that
Flannery's plans, which it believes are based on misconceptions and ignorance of
our  businesses,  are  fatally  flawed  and  reflect  Flannery's  desire  for  a
multi-million dollar commission on the breakup of your Company.

     Your Board unanimously opposes the Flannery solicitation and strongly urges
you  not  to  return any white consent cards.  Instead, please show your support
for management and its turnaround strategy  by signing, dating and returning the
enclosed GREEN revocation of consent card with a vote to REVOKE CONSENT today!

     As evidenced by the enclosed letter, Oakville, N.V., one of  the  Company's
largest  shareholders,  which  had  supported  prior  efforts  to remove certain
directors, now fully supports Tesoro's  management team and its current program.
Steven H. Grapstein, Vice Chairman of the Company's Board  of  Directors,  is  a
director and vice president of Oakville, N.V.

THE TESORO TURNAROUND:  .  RESURGENT OPERATING PROFITS
                        .  INCREASED STOCK PRICE
                        .  SHARPLY REDUCED DEBT
                        .  IMPROVED CORPORATE GOVERNANCE

     The  fruits  of our turnaround strategy are becoming more and more apparent
and hold the potential  to  significantly  improve future performance.  Enclosed
with this letter are graphs which demonstrate our success since 1992:  operating
profit increased tenfold; stock price nearly tripled; and total debt was cut  by
over $100 million, or 40 percent.

     Financial  restructuring has been an important component of the turnaround.
Our efforts to reorganize the Company,  restructure its finances and reduce debt
and costs will continue.

     Our turnaround strategy has also placed each of our three businesses  on  a
course to improve profits and future prospects:

     .    Our   Exploration   and   Production   operations   achieved
          outstanding  operating  profits  during the last three years
          and continue to develop  existing properties and explore for
          reserves with excellent success rates at low costs;

     .    The Refining and Marketing operations have been improved  by
          shifting  production to higher-margin products and expanding
          our marketing efforts;

     .    The Oil Field Supply  and  Distribution operations have been
          restructured by streamlining core operations and by  selling
          unprofitable   land-based   operations.   In  addition,  the
          Company has  recently  acquired  Coastwide  Energy Services,
          Inc. Management believes that  the  combining  of  Coastwide
          with   the   Company's   existing   oil   field  supply  and
          distribution operations will generate significantly improved
          results from these operations in the future.

     To help our  strategy  continue  to  produce  shareholder value, management
commenced a study of corporate governance guidelines in early December 1995.  As
a result of this  study  and  the  recommendations  of  management,  your  Board
recently  adopted  corporate  governance  guidelines  designed  to  further  the
responsiveness of the Board to the shareholders.

THE FLANNERY GROUP'S PLAN:  .  MISCONCEPTIONS
                            .  IGNORANCE
                            .  SELF INTEREST

                                       2

     Your  Board believes that the arguments set forth by the Flannery Group are
seriously flawed and misleading  and  that  the Flannery Group's proposed agenda
for the Company  is  totally  unrealistic,  is  based  upon  misconceptions  and
ignorance  of  Tesoro's  business and our industry and has little bearing on the
real choices  facing  Tesoro.   Worse,  Mr.  Flannery--who  has  already led two
unsuccessful  attempts  to  take  over  Tesoro--appears  to  be   motivated   by
self-interest at the expense of the other Tesoro stockholders.

     Simply compare the Flannery Plan to Tesoro's reality:

FLANNERY PLAN:
Divest the Alaska refinery

     TESORO REALITY:
     --------------------------------------------------------------------

     This  is not the time to sell the refinery.  The industry cycle is at
     a low point and any sale now of the Alaska refinery would, management
     believes, only result in a fire-sale price.

     Many refineries that have  been  put  up  for sale by other companies
     have either been withdrawn from the market or shut down.

     A sale at current market prices would almost certainly not cover  the
     refinery's  $90  million in debt or the environmental clean-up costs,
     let alone leave excess funds to pay other debt.

     A sale at current market prices  would also wipe out the value gained
     by recent improvements in the refinery operations and  would  prevent
     shareholders  from  participating in the cyclical turnaround expected
     by analysts and industry experts.

FLANNERY PLAN:
Reduce or refinance high cost debt.

     TESORO REALITY:
     --------------------------------------------------------------------

     Total debt has already been reduced  by 40%, over $100 million, since
     1992.

     As part of its debt reduction program, Tesoro recently redeemed $34.6
     million of its 12 3/4% subordinated debentures.

     Without an improvement in our credit  rating,  the  costs  associated
     with  a  refinancing would, management believes, more than offset any
     interest savings.

     Tesoro has been in discussions  since  fall 1995 on restructuring and
     refinancing our $79 million debt with the State of Alaska.

                                       3

     Unlike your Board, the individuals who comprise the Flannery Group are  not
corporate  builders  or creators of shareholder value.  Their goal appears to be
to dismantle the Company or auction it  off to the highest bidder.  Moreover, as
Kevin Flannery was forced to reveal in a  deposition  under  oath,  in  previous
unauthorized attempts to sell your Company, it was his expectation that he would
receive a multi-million dollar commission for breaking up your Company.

     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 the Company, which will have no legal effect but would assist us
in monitoring the progress of the Flannery Group's consent solicitation.

     Remember:   This  attempt  to  take  over Tesoro, the Board believes, would
deprive the stockholders of  the  opportunity  to  benefit from the progress now
underway at Tesoro.

                              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

                                       4

                                 OAKVILLE, N.V.
                                767 Third Avenue
                               New York, NY 10017

  February 21, 1996

  Mr. Bruce A. Smith
  Tesoro Petroleum Corporation
  8700 Tesoro Drive
  San Antonio, TX 78217

  Dear Bruce:

  I am writing to you as director and on behalf of Oakville, N.V., an  affiliate
  of  Kuo Investment Limited, Tesoro's second largest shareholder with a holding
  of approximately 6%.

  As I have discussed with you, we are pleased with the turnaround that has been
  underway at the company, which has  begun to show very satisfying results.  We
  believe that implementing management's current strategy is the  best  one  for
  Tesoro's  shareholders  and  will  lead  to further improvements.  We are also
  pleased with certain governance  changes  which have recently been implemented
  by the Board.

  As a result of these positive developments at the company, we have decided  to
  fully  support Tesoro's management in opposing the consent solicitation of the
  dissident group led by Kevin Flannery of Whelan Management nor will we support
  Flannery or his  candidates  at  the  next  Annual  Meeting.   In the past two
  elections, Oakville N.V. has voted for some of Mr. Flannery's nominees  in  an
  effort  to  bring  change to Tesoro's Board of Directors.  However, we believe
  that the proposed governance  policies,  director succession plans, management
  changes and current strategy are moving Tesoro on a path which is in the  best
  interest  of all shareholders.  We are encouraged by these positive trends and
  urge all shareholders who have supported the dissidents in the past to join us
  in support of management in its efforts to continue with its current program.

  You may provide a copy of  this  letter  to the company's shareholders to show
  our support and you may refer to this letter in  connection  with  information
  sent to Tesoro's shareholders, including any consent solicitation material.

  Sincerely yours,

  /s/  Steven H. Grapstein

  Steven H. Grapstein, Director
     Oakville N.V.