Exhibit 99.1

                    Tesoro First Quarter Earnings Rise 150%

     SAN ANTONIO--(BUSINESS WIRE)--May 6, 2004--Tesoro Petroleum Corporation
(NYSE:TSO) today reported record net earnings of $50.4 million, or $0.75 per
share, for the first quarter of 2004 compared to net earnings of $20.4 million,
or $0.32 per share, for the first quarter of 2003.
     "Net earnings were 150% better than last year's first quarter results and
the best first quarter results in the history of Tesoro," said Bruce A. Smith,
chairman, president and CEO of Tesoro. "Seasonally, product demand is weaker
during the first quarter in our markets, but this year, strong demand in
combination with below-average product inventories created better-than-normal
industry refining margins in all our refining regions. Given the market
environment, we increased total refining throughput to capture the higher
margin. Good reliability was a key factor in our success this quarter, even
though we had some unscheduled downtime at our California refinery."
     "Net earnings also benefited from lower interest expense as a result of the
debt reduction we achieved last year. Our goal is to continue to improve
profitability and use free cash flow to reduce debt. The successful completion
of our consent solicitation in March gives us greater flexibility to repay
debt," stated Smith.

     Public Invited to Listen to Analyst Conference Call via Internet

     At 2 p.m., CDT, Thursday, May 6, 2004, Tesoro will broadcast, live, its
conference call with analysts regarding first quarter 2004 results. Interested
parties may listen to the live conference call over the Internet by logging on
to Tesoro's Internet site at http://www.tesoropetroleum.com and clicking on the
"What's New" section.

     Tesoro Petroleum Corporation, a Fortune 500 Company, is an independent
refiner and marketer of petroleum products. Tesoro operates six refineries in
the western United States with a combined capacity of nearly 560,000 barrels per
day. Tesoro's retail-marketing system includes approximately 550 branded retail
stations, of which over 200 are company operated under the Tesoro(R) and
Mirastar(R) brands.

     This news release contains certain statements that are "forward-looking"
statements within the meaning of Section 27A of the Securities Act of 1933 and
Section 21E of the Securities Exchange Act of 1934. These forward-looking
statements concern the company's goals of improving profitability, generating
free cash flow and reducing debt. Factors which can cause actual results to
differ from these forward-looking statements include: changes in general
economic conditions, the timing and extent of changes in demand for refined
products, availability and cost of crude oil, other feedstocks or refined
products, throughput and yield levels, disruptions due to equipment
interruptions or failure at our or third-party facilities and other factors
beyond our control. For more information concerning these factors and other
factors that could cause such a difference, see our annual report on Form 10-K
and quarterly reports on Form 10-Q, filed with the Securities and Exchange
Commission. We undertake no obligation to publicly release the result of any
revisions to any such forward-looking statements that may be made to reflect
events or circumstances that occur, or which we become aware of, after the date
hereof.


                          TESORO PETROLEUM CORPORATION
                      STATEMENT OF CONSOLIDATED OPERATIONS
                                   (Unaudited)
                      (In million except per share amounts)


                                    Three Months Ended
                                         March 31,
                                    2004          2003 (a)
                                -------------   ------------

Revenues                         $  2,429.9     $ 2,286.1

Costs and Expenses:
      Costs of sales and
       operating expenses           2,234.7       2,131.1
      Selling, general and
       administrative expenses         31.0          38.3
      Depreciation and
       amortization                    37.0          37.0
      Loss on asset sales and
       impairments                      0.6           0.2
                                -------------   ------------
Operating Income                      126.6          79.5
      Interest and Financing
       Costs, Net (b)                 (42.9)        (47.0)
                                -------------   ------------
         Earnings Before
          Income Taxes                 83.7          32.5
Income Tax Provision                   33.3          12.1
                                -------------   ------------
Net Earnings                     $     50.4     $    20.4
                                =============     ============
Net Earnings Per Share:
      Basic                      $     0.78     $    0.32
      Diluted                    $     0.75     $    0.32

Weighted Average Common Shares:
      Basic                            65.0          64.6
      Diluted                          67.3          64.7
- ---------------------
(a) The 2003 results include the Marine Services operations, which
    were sold in December 2003.

(b) In March 2004 the Company amended both the 8% senior secured
    notes and the senior secured term loans resulting in pretax
    financing expenses of $2.5 million.


                          TESORO PETROLEUM CORPORATION
                         SELECTED OPERATING SEGMENT DATA
                                   (Unaudited)
                                  (In millions)


                                 Three Months Ended
                                      March 31,
                               ------------------------
                                   2004         2003
                               ------------  ----------
Operating Income
   Refining                   $      151.6  $    109.2
   Retail                             (4.2)       (8.1)
   Marine Services (a)                   -         1.1
                               ------------  ----------
          Total Segment
           Operating Income          147.4       102.2
   Corporate and
    Unallocated Costs (c)            (20.2)      (22.5)
   Loss on Asset Sales and
    Impairments                       (0.6)       (0.2)
                               ------------  ----------
       Operating Income              126.6        79.5
   Interest and Financing
    Costs, Net (b)                   (42.9)      (47.0)
                               ------------  ----------
       Earnings Before
        Income Taxes          $       83.7  $     32.5
                               ============  ==========

Depreciation and Amortization
   Refining                   $       31.0  $     29.8
   Retail                              4.4         5.0
   Marine Services (a)                  --         0.7
   Corporate                           1.6         1.5
                               -----------   ----------
       Depreciation and
        Amortization          $       37.0  $     37.0
                               ============  ==========

Capital Expenditures
   Refining                   $       14.5  $     27.0
   Retail                              0.1         0.2
   Marine Services (a)                  --         0.3
   Corporate                           0.3         0.2
                               ------------  ----------

       Capital Expenditures   $       14.9   $     27.7
                               ============  ==========

- ----------------------
(c) Corporate and unallocated costs in 2003 include charges of
    $4.7 million in reorganization costs, primarily a non-cash charge
    for voluntary early retirement benefits and severance payments. An
    additional $4.3 million of reorganization costs were charged to
    the operating segments during 2003, including $2.6 million in
    Refining, $1.3 million in Retail and $0.4 million in Marine
    Services.


                               BALANCE SHEET DATA
                                   (Unaudited)
                              (Dollars in millions)

                                       March 31,       December 31,
                                         2004              2003
                                     -------------    --------------

      Total Assets                  $      3,841.8    $      3,661.3
      Total Debt                    $      1,610.2    $      1,608.8
      Total Stockholders' Equity    $      1,021.1    $        965.4
      Total Debt to Capitalization
       Ratio                                    61%              62%



                          TESORO PETROLEUM CORPORATION
                                 OPERATING DATA
                                   (Unaudited)


                                            Three Months Ended
                                                 March 31,
                                           ---------------------
                                              2004       2003
                                           ----------- ---------
REFINING SEGMENT
  Total Refining Segment
   Throughput (thousand barrels per day)
   Heavy crude                                  272.0     282.9
   Light crude                                  211.6     167.5
   Other feedstocks                              14.1      14.1
                                           ----------- ---------
           Total Throughput                     497.7     464.5
                                           =========== =========

  Yield (thousand barrels per day)
   Gasoline and gasoline blendstocks            245.8     229.8
   Jet fuel                                      64.1      56.5
   Diesel fuel                                  103.4      97.7
   Heavy oils, residual products,
    internally produced fuel
      and other                                 104.3     100.0
                                           ----------- ---------
           Total Yield                          517.6     484.0
                                           =========== =========

  Refining Margin ($/throughput bbl) (d)
   Gross                                  $      7.58 $    6.92
   Manufacturing cost before depreciation
    and amortization (e)                  $      2.88 $    2.90

  Segment Operating Income ($ millions)
   Gross refining margin (after inventory
    changes) (f)                          $     348.0 $   294.8
   Expenses
    Manufacturing costs                         130.5     121.3
    Other operating expenses                     29.5      26.4
    Selling, general and administrative           5.4       8.1
    Depreciation and amortization (g)            31.0      29.8
                                           ----------- ---------
        Segment Operating Income          $     151.6 $   109.2
                                           =========== =========

  Product Sales (thousand barrels per
   day) (h)
    Gasoline and gasoline blendstocks           289.4     270.0
    Jet fuel                                     79.5      87.3
    Diesel fuel                                 119.8     123.5
    Heavy oils, residual products and
     other                                       75.8      62.7
                                           ----------- ---------
           Total Product Sales                  564.5     543.5
                                           =========== =========

  Product Sales Margin ($/barrel) (h)
   Average sales price                    $     44.98 $   42.59
   Average costs of sales                       37.90     36.60
                                           ----------- ---------
    Product Sales Margin                  $      7.08 $    5.99
                                           =========== =========

- -----------------------------------------
(d) Management uses gross refining margin per barrel to compare
    profitability to other companies in the industry.  Gross
    refining margin per barrel is calculated by dividing gross
    refining margin by total refining throughput and may not be
    calculated similarly by other companies.

(e) Management uses manufacturing costs per barrel to evaluate
    the efficiency of refinery operations.  Manufacturing costs per
    barrel may not be comparable to similarly titled measures used
    by other companies.

(f) Gross refining margin is revenues less cost of refining
    feedstock, which approximates total Refining segment throughput
    times gross refining margin per barrel, adjusted for changes in
    refined product inventory due to selling a volume and mix of
    product that is different than actual volumes manufactured.
    Also includes the effect of intersegment sales to the Retail
    segment at prices which approximate market.

(g) Includes manufacturing depreciation and amortization per
    throughput barrel of approximately $0.60 and $0.62 for the
    three months ended March 31, 2004 and 2003, respectively.

(h) Sources of total product sales include products manufactured
    at the refineries, products drawn from inventory balances and
    products purchased from third parties. Total product sales
    margin includes margins on sales of manufactured and purchased
    products and the effects of inventory changes.


                          TESORO PETROLEUM CORPORATION
                                 OPERATING DATA
                                   (Unaudited)




                                          Three Months Ended
                                               March 31,
                                          -------------------
                                            2004       2003
                                          ---------  --------
Refining By Region
   California
     Throughput (thousand barrels per
      day)
       Heavy crude                           144.4     149.8
       Light crude                             4.0       3.8
       Other feedstocks                        4.8       4.2
                                          ---------  --------
             Total Throughput                153.2     157.8
                                          =========  ========

     Yield (thousand barrels per day)
       Gasoline and gasoline blendstocks      97.7     100.9
       Diesel fuel                            37.0      39.6
       Heavy oils, residual products,
        internally produced fuel
         and other                            28.1      27.4
                                          ---------  --------
             Total Yield                     162.8     167.9
                                          =========  ========

     Refining Margin ($/throughput bbl)
       Gross                             $   11.10  $  10.56
       Manufacturing cost before
        depreciation and amortization    $    4.61  $   4.27

   Pacific Northwest (Alaska &
    Washington)
     Throughput (thousand barrels per
      day)
       Heavy crude                            84.4      79.6
       Light crude                            72.9      62.9
       Other feedstocks                        5.2       7.4
                                          ---------  --------
             Total Throughput                162.5     149.9
                                          =========  ========

     Yield (thousand barrels per day)
       Gasoline and gasoline blendstocks      69.3      66.3
       Jet fuel                               28.7      25.0
       Diesel fuel                            26.7      23.0
       Heavy oils, residual products,
        internally produced fuel
          and other                           42.5      40.9
                                          ---------  --------
             Total Yield                     167.2     155.2
                                          =========  ========

     Refining Margin ($/throughput bbl)
       Gross                             $    6.44  $   6.19
       Manufacturing cost before
        depreciation and amortization    $    2.38  $   2.45

   Mid-Pacific
    (Hawaii)
     Throughput (thousand barrels per
      day)
       Heavy crude                            43.2      53.5
       Light crude                            41.2      21.9
                                          ---------  --------
             Total Throughput                 84.4      75.4
                                          =========  ========

     Yield (thousand barrels per day)
       Gasoline and gasoline blendstocks      23.2      17.7
       Jet fuel                               24.7      23.4
       Diesel fuel                            15.0      12.7
       Heavy oils, residual products,
        internally produced fuel
          and other                           23.0      22.8
                                          ---------  --------
             Total Yield                      85.9      76.6
                                          =========  ========

     Refining Margin ($/throughput bbl)
       Gross                             $    4.54  $   3.15
       Manufacturing cost before
        depreciation and amortization    $    1.32  $   1.40


                          TESORO PETROLEUM CORPORATION
                                 OPERATING DATA
                                   (Unaudited)



                                       Three Months Ended
                                            March 31,
                                      --------------------
                                         2004       2003
                                      ---------  ---------
   Mid-Continent (North Dakota &
    Utah) (i)
     Throughput (thousand barrels per
      day)
       Light crude                        93.5       78.9
       Other feedstocks                    4.1        2.5
                                      ---------  ---------
             Total Throughput             97.6       81.4
                                      =========  =========

     Yield (thousand barrels per day)
       Gasoline and gasoline
        blendstocks                       55.6       44.9
       Jet fuel                           10.7        8.1
       Diesel fuel                        24.7       22.4
       Heavy oils, residual products,
        internally produced fuel
          and other                       10.7        8.9
                                      ---------  ---------
             Total Yield                 101.7       84.3
                                      =========  =========

     Refining Margin ($/throughput
      bbl)
       Gross                         $    6.54  $    4.71
       Manufacturing cost before
        depreciation and
         amortization                $    2.35  $    2.47

- -------------
(i) Throughput and yield levels were reduced in the 2003 quarter
    during a scheduled maintenance turnaround at the Utah refinery.


                          TESORO PETROLEUM CORPORATION
                                 OPERATING DATA
                                   (Unaudited)


                                     Three Months Ended
                                           March 31,
                                    ----------------------
                                        2004        2003
                                    ------------ ---------
RETAIL SEGMENT
  Number of Stations (end of
   period)
    Company-operated                        224       230
    Branded jobber/dealer                   324       354
                                    ------------ ---------
     Total Stations                         548       584
                                    ============ =========
  Average Stations (during
   period)
    Company-operated                        225       231
    Branded jobber/dealer                   326       360
                                    ------------ ---------
     Total Average Retail Stations          551       591
                                    ============ =========

  Fuel Sales (millions of
   gallons)
    Company-operated                       69.6      77.1
    Branded jobber/dealer                  53.3      66.6
                                    ------------ ---------
          Total Fuel Sales                122.9     143.7
                                    ============ =========

  Fuel Margin ($/gallon) (j)       $       0.14  $   0.11
  Merchandise Sales ($ millions)   $       28.2  $   24.9
  Merchandise Margin ($ millions)  $        7.3  $    6.2
  Merchandise Margin %                      26%       25%

  Segment Operating Income (Loss)
   ($ millions)
    Gross Margins
     Fuel (k)                      $       17.5 $    16.4
     Merchandise and other non-
      fuel margin                           8.2       7.3
                                    ------------ ---------
        Total Gross Margins                25.7      23.7
    Expenses
     Operating expenses                    18.5      18.4
     Selling, general and
      administrative                        7.0       8.4
     Depreciation and amortization          4.4       5.0
                                    ------------ ---------
     Segment Operating Income
      (Loss)                       $       (4.2)$    (8.1)
                                    ============ =========

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

(j) Fuel margin per gallon is calculated by dividing fuel gross
    margin by fuel sales volumes. Fuel margin per gallon may not
    be calculated similarly by other companies. Management uses
    fuel margin per gallon calculations to compare profitability
    to other companies in the industry.

(k) Includes the effect of intersegment purchases from the Refining
    segment at prices which approximate market.


    CONTACT: Tesoro Petroleum Corporation, San Antonio
             Investors:
             John Robertson, 210-283-2687
             or
             Media:
             Tara Ford, 210-283-2676