Exhibit 99.1

Tesoro Corporation Announces First Quarter Results

    SAN ANTONIO--(BUSINESS WIRE)--May 4, 2006--Tesoro Corporation
(NYSE:TSO) today reported net earnings of $43 million, or $0.61 per
share for the first quarter of 2006 up 54% from net earnings of $28
million, or $0.40 per share for the first quarter of 2005.
    Results for the first quarter 2006 included after-tax charges of
$4 million, or $0.06 per share, primarily relating to the previously
announced sale of 13 retail sites in western Washington.
    "Tesoro's first quarter earnings improvement was a significant
achievement considering weaker market conditions, higher energy costs,
the substantial turnaround work at our Golden Eagle refinery and the
slow-down at our Alaska refinery due to extreme icing in the Cook
Inlet," said CEO Bruce Smith. "During January and February's low
margin environment, we completed the ultra low sulfur diesel project
at Golden Eagle and additional maintenance that enabled us to optimize
throughput and yields in March when margins improved."
    The company's increase in net earnings during the 2006 first
quarter compared to the prior year was primarily due to higher
throughput levels, lower interest expense as a result of debt
reduction and refinancing in 2005, and decreased corporate general and
administrative expenses.
    "By focusing on operational excellence, Tesoro continues to
demonstrate operational success and reliability. One example of the
focus on excellence was our employees' rapid response to the
mid-February incident in Alaska. This demonstrates the respect we have
for the environment and our focus on safe operations," Smith said.
"Reliability is a key to profitability and we are focused on
maximizing our production to supply our customers during the driving
season."

    Board Declares Quarterly Dividend

    Tesoro announced today that its Board of Directors has approved
the regular quarterly cash dividend of $0.10 per share. The dividend
is payable June 15, 2006 to shareholders of record as of June 1, 2006.

    Public Invited to Listen to Analyst Conference Call via Internet

    At 3:00 p.m., CDT, Thursday, May 4, 2006, Tesoro will broadcast,
live, its conference call with analysts regarding first quarter 2006
results. Interested parties may listen to the live conference call
over the Internet by logging on to Tesoro's Internet site at
http://www.tsocorp.com.
    Tesoro Corporation, a Fortune 200 Company, is an independent
refiner and marketer of petroleum products. Tesoro operates six
refineries in the western United States with a combined capacity of
approximately 560,000 barrels per day. Tesoro's retail-marketing
system includes nearly 475 branded retail stations, of which over 200
are company owned and operated under the Tesoro(R) and Mirastar(R)
brands.


                          TESORO CORPORATION
                STATEMENTS OF CONSOLIDATED OPERATIONS
                             (Unaudited)
                (In millions except per share amounts)


                                                       Three Months
                                                           Ended
                                                         March 31,
                                                     -----------------
                                                      2006      2005
                                                     -------   -------
Revenues                                            $ 3,877   $ 3,171
Costs and Expenses:
     Costs of sales and operating expenses            3,689     2,997
     Selling, general and administrative
      expenses (a)                                       40        54
     Depreciation and amortization                       60        41
     Loss on asset disposals and impairments              7         1
                                                     -------   -------
Operating Income                                         81        78
Interest and Financing Costs                            (20)      (32)
Interest Income and Other                                10         1
                                                     -------   -------
      Earnings Before Income Taxes                       71        47
Income Tax Provision                                     28        19
                                                     -------   -------
Net Earnings                                        $    43   $    28
                                                     =======   =======
Net Earnings Per Share:
     Basic                                          $  0.63   $  0.41
     Diluted                                        $  0.61   $  0.40
Weighted Average Common Shares:
     Basic                                             68.5      66.8
     Diluted                                           70.6      70.1

- ------------
(a) Includes stock-based and other compensation charges totaling $11
    million during the 2005 first quarter, related to the termination
    and retirement of certain executive officers.


               NET EARNINGS ADJUSTED FOR SPECIAL ITEMS
                             (Unaudited)
                (In millions except per share amounts)


                                                       Three Months
                                                           Ended
                                                         March 31,
                                                     -----------------
                                                      2006      2005
                                                     -------   -------
Net Earnings - U.S. GAAP                            $    43   $    28
Special Items, After-tax:
     Termination and retirement costs (a)                 -         6
                                                     -------   -------
Net Earnings Adjusted for Special Items             $    43   $    34
                                                     =======   =======

Net Earnings Per Share - U.S. GAAP                  $  0.61   $  0.40
Special Items Per Share, After-tax:
     Termination and retirement costs (a)                 -      0.09
                                                     -------   -------
Net Earnings Per Share Adjusted for Special Items   $  0.61   $  0.49
                                                     =======   =======

- ------------
Note: The special items present information that the Company believes
      is useful to investors.  The Company believes that the special
      items described above are not indicative of its core operations.


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


                                                       Three Months
                                                           Ended
                                                         March 31,
                                                     -----------------
                                                      2006      2005
                                                     -------    ------
Operating Income (Loss)
 Refining                                           $   125    $  132
 Retail                                                 (12)      (11)
                                                     -------    ------
        Total Segment Operating Income                  113       121
 Corporate and Unallocated Costs (a)                    (32)      (43)
                                                     -------    ------
  Operating Income                                       81        78
 Interest and Financing Costs                           (20)      (32)
 Interest Income and Other                               10         1
                                                     -------    ------
  Earnings Before Income Taxes                      $    71    $   47
                                                     =======    ======

Depreciation and Amortization
 Refining                                           $    54    $   35
 Retail                                                   4         4
 Corporate                                                2         2
                                                     -------    ------
        Depreciation and Amortization               $    60    $   41
                                                     =======    ======

Capital Expenditures
 Refining                                           $    55    $   37
 Retail                                                   1         -
 Corporate                                                2        27
                                                     -------    ------
        Capital Expenditures                        $    58    $   64
                                                     =======    ======


                          BALANCE SHEET DATA
                             (Unaudited)
                        (Dollars in millions)


                                          March 31,      December 31,
                                            2006             2005
                                         ------------    -------------
Cash and Cash Equivalents               $        306    $         440
Total Assets                            $      5,080    $       5,097
Total Debt                              $      1,049    $       1,047
Total Stockholders' Equity              $      1,869    $       1,887
Total Debt to Capitalization Ratio                36%              36%


                          TESORO CORPORATION
                            OPERATING DATA
                             (Unaudited)


                                                   Three Months Ended
                                                        March 31,
                                                   -------------------
                                                    2006       2005
                                                   --------   --------
REFINING SEGMENT
 Total Refining Segment
  Throughput (thousand barrels per day)
   Heavy crude                                         244        263
   Light crude                                         238        188
   Other feedstocks                                     15         26
                                                   --------   --------
          Total Throughput                             497        477
                                                   ========   ========

  Yield (thousand barrels per day)
   Gasoline and gasoline blendstocks                   234        223
   Jet fuel                                             69         65
   Diesel fuel                                         100         91
   Heavy oils, residual products, internally
    produced fuel and other                            114        116
                                                   --------   --------
          Total Yield                                  517        495
                                                   ========   ========

  Refining Margin ($/throughput bbl) (b)
   Gross                                          $   8.52   $   8.37
   Manufacturing cost before depreciation and
    amortization (b)                              $   3.77   $   3.55

  Segment Operating Income ($ millions)
   Gross refining margin (after inventory
    changes) (c)                                  $    395   $    367
   Expenses
    Manufacturing costs                                169        153
    Other operating expenses                            39         39
    Selling, general and administrative                  5          7
    Depreciation and amortization (d)                   54         35
    Loss on asset disposals and impairments              3          1
                                                   --------   --------
         Segment Operating Income                 $    125   $    132
                                                   ========   ========

  Product Sales (thousand barrels per day) (e)
   Gasoline and gasoline blendstocks                   271        267
   Jet fuel                                             91         96
   Diesel fuel                                         125        123
   Heavy oils, residual products and other              82         69
                                                   --------   --------
          Total Product Sales                          569        555
                                                   ========   ========

  Product Sales Margin ($/barrel) (e)
   Average sales price                            $  73.36   $  59.09
   Average costs of sales                            65.78      51.36
                                                   --------   --------
     Product Sales Margin                         $   7.58   $   7.73
                                                   ========   ========

- ------------
(b) Management uses gross refining margin per barrel to evaluate
    performance, allocate resources and compare profitability to other
    companies in the industry. Gross refining margin per barrel is
    calculated by dividing gross refining margin before inventory
    changes by total refining throughput and may not be calculated
    similarly by other companies. Management uses manufacturing costs
    per barrel to evaluate the efficiency of refinery operations and
    allocate resources. Manufacturing costs per barrel may not be
    comparable to similarly titled measures used by other companies.
    Investors and analysts use these financial measures to help
    analyze and compare companies in the industry on the basis of
    operating performance. These financial measures should not be
    considered as alternatives to segment operating income, revenues,
    costs of sales and operating expenses or any other measure of
    financial performance presented in accordance with accounting
    principles generally accepted in the United States of America.

(c) Gross refining margin is revenues less costs of refining
    feedstocks, purchased products, transportation and distribution.
    Gross refining margin 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.

(d) Includes manufacturing depreciation and amortization per
    throughput barrel of approximately $1.11 and $0.73 for the three
    months ended March 31, 2006 and 2005, respectively.

(e) 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 CORPORATION
                            OPERATING DATA
                             (Unaudited)


                                                   Three Months Ended
                                                       March 31,
                                                   ------------------
                                                    2006       2005
                                                   --------   -------
Refining By Region
 California (f)
  Throughput (thousand barrels per day)
   Heavy crude                                         139       144
   Light crude                                           5         -
   Other feedstocks                                      8         5
                                                   --------   -------
          Total Throughput                             152       149
                                                   ========   =======

  Yield (thousand barrels per day)
   Gasoline and gasoline blendstocks                    91        82
   Diesel fuel                                          37        40
   Heavy oils, residual products, internally
    produced fuel and other                             34        34
                                                   --------   -------
          Total Yield                                  162       156
                                                   ========   =======

  Refining Margin ($/throughput bbl)
   Gross                                          $  13.26   $ 16.58
   Manufacturing cost before depreciation and
    amortization                                  $   6.06   $  5.54

 Pacific Northwest (Alaska & Washington) (f)
  Throughput (thousand barrels per day)
   Heavy crude                                          84        81
   Light crude                                          66        42
   Other feedstocks                                      4        17
                                                   --------   -------
          Total Throughput                             154       140
                                                   ========   =======

  Yield (thousand barrels per day)
   Gasoline and gasoline blendstocks                    65        62
   Jet fuel                                             29        28
   Diesel fuel                                          20        12
   Heavy oils, residual products, internally
    produced fuel and other                             45        44
                                                   --------   -------
          Total Yield                                  159       146
                                                   ========   =======

  Refining Margin ($/throughput bbl)
   Gross                                          $   7.20   $  4.57
   Manufacturing cost before depreciation and
    amortization                                  $   3.18   $  3.20

 Mid-Pacific (Hawaii)
  Throughput (thousand barrels per day)
   Heavy crude                                          21        38
   Light crude                                          65        46
                                                   --------   -------
          Total Throughput                              86        84
                                                   ========   =======

  Yield (thousand barrels per day)
   Gasoline and gasoline blendstocks                    22        20
   Jet fuel                                             29        26
   Diesel fuel                                          13        12
   Heavy oils, residual products, internally
    produced fuel and other                             24        27
                                                   --------   -------
          Total Yield                                   88        85
                                                   ========   =======

  Refining Margin ($/throughput bbl)
   Gross                                          $   3.23   $  4.04
   Manufacturing cost before depreciation and
    amortization                                  $   1.56   $  1.67

- ------------
(f) The Company experienced reduced throughput and yields during
    scheduled maintenance turnarounds for the California refinery
    during the 2006 and 2005 first quarters and the Washington
    refinery during the 2005 first quarter.


                          TESORO CORPORATION
                            OPERATING DATA
                             (Unaudited)


                                                       Three Months
                                                           Ended
                                                         March 31,
                                                     -----------------
                                                      2006      2005
                                                     -------   -------
 Mid-Continent (North Dakota & Utah)
  Throughput (thousand barrels per day)
   Light crude                                          102       100
   Other feedstocks                                       3         4
                                                     -------   -------
          Total Throughput                              105       104
                                                     =======   =======

  Yield (thousand barrels per day)
   Gasoline and gasoline blendstocks                     56        59
   Jet fuel                                              11        11
   Diesel fuel                                           30        27
   Heavy oils, residual products, internally
    produced fuel and other                              11        11
                                                     -------   -------
          Total Yield                                   108       108
                                                     =======   =======

  Refining Margin ($/throughput bbl)
   Gross                                            $  8.17   $  5.08
   Manufacturing cost before depreciation and
    amortization                                    $  3.18   $  2.69


                          TESORO CORPORATION
                            OPERATING DATA
                             (Unaudited)


                                                       Three Months
                                                           Ended
                                                         March 31,
                                                     -----------------
                                                      2006      2005
                                                     -------   -------
RETAIL SEGMENT
   Number of Stations (end of period)
    Company-operated                                    210       215
    Branded jobber/dealer                               260       289
                                                     -------   -------
     Total Stations                                     470       504
                                                     =======   =======

   Average Stations (during period)
    Company-operated                                    210       215
    Branded jobber/dealer                               263       291
                                                     -------   -------
     Total Average Retail Stations                      473       506
                                                     =======   =======

   Fuel Sales (millions of gallons)
    Company-operated                                     59        65
    Branded jobber/dealer                                40        46
                                                     -------   -------
          Total Fuel Sales                               99       111
                                                     =======   =======

   Fuel Margin ($/gallon) (g)                       $  0.15   $  0.12
   Merchandise Sales ($ millions)                   $    32   $    30
   Merchandise Margin ($ millions)                  $     8   $     8
   Merchandise Margin %                                  25%       25%

   Segment Operating Loss ($ millions)
    Gross Margins
     Fuel (h)                                       $    15   $    13
     Merchandise and other non-fuel margin                9         8
                                                     -------   -------
      Total Gross Margins                                24        21
    Expenses
     Operating expenses                                  22        22
     Selling, general and administrative                  6         6
     Depreciation and amortization                        4         4
     Loss on asset disposals and impairments              4         -
                                                     -------   -------
      Segment Operating Loss                        $   (12)  $   (11)
                                                     =======   =======

- ------------
(g) Management uses fuel margin per gallon to compare profitability to
    other companies in the industry. Investors and analysts use fuel
    margin per gallon to help analyze and compare companies in the
    industry on the basis of operating performance. 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.

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

    CONTACT: Tesoro Corporation, San Antonio
             Investors:
             Scott Phipps, 210-283-2882
             or
             Media:
             Sarah Simpson, 210-283-2374