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



                        TESORO REPORTS ITS BEST RESULTS
                             IN MORE THAN A DECADE

     San Antonio,  Texas  --  Jan.  30,  1996  --  Tesoro  Petroleum Corporation
(NYSE:TSO) today announced 1995 net earnings applicable to common stock of $54.6
million, or $2.18 per share, compared with $13.0 million, or $.56 per  share  in
1994.   Operating  profit reached $105.9 million, compared with $64.4 million in
1994.  These results represent  the  company's  best  performance in more than a
decade, and were  achieved  despite  very  difficult  industry  conditions  that
prevailed through most of the year.

     The  1995  results  included an after-tax gain of approximately $33 million
($1.34 per share) from the sale  of  certain  interests in the Bob West field in
south Texas, partially offset by charges of approximately $5 million  ($.21  per
share)  for  employee  terminations  and  restructuring and $3 million ($.11 per
share) for the early extinguishment of  debt.  The 1994 results included an $8.5
million ($.37 per share) refund from the resolution of a refining and  marketing
tariff  issue,  partially offset by a $5 million ($.21 per share) charge for the
early extinguishment of debt.   Excluding  the  gain  on  sale of Bob West field
interests, 1995 results were the best in five years.

     "Achieving these results in the face of depressed natural gas and petroleum
refining industry conditions speaks loudly for the changes we have  effected  at
Tesoro,"  President  and Chief Executive Officer Bruce Smith said.  "Initiatives
within our core operations,  coupled  with  company-wide efficiency measures and
lower debt levels, are expected to help continue Tesoro's improvements.  Only  a
small portion of the benefits we expect from these efforts was realized in 1995,
but they should have a much larger impact in 1996 and beyond."

     Tesoro's  enhanced 1995 results were primarily attributable to improvements
within its Exploration  &  Production  (E&P)  segment,  specifically relating to
natural  gas  operations  in  south  Texas.   These  operations  benefited  from
continued development of the Bob West field, despite natural gas  market  prices
that  averaged  almost  10  percent lower than in 1994.  Excluding the gain from
sale of certain Bob  West  field  interests  earlier  in the year, the segment's
operating profit rose 18 percent from 1994 to $76 million as total domestic  and
Bolivian  natural  gas  production  increased  26  percent  to an average of 133
million cubic feet per day.

     The Refining & Marketing (R&M) segment  had operating profit of $.7 million
in 1995, reflecting a strong recovery from more than  $7  million  of  operating
losses  through  the first half of the year, when industry refining margins were
among the lowest  in  a  decade.   These  results  compare  with  a $2.4 million
operating profit in 1994.

                                     -more-

     Stronger product prices and a more advantageous feedstock mix in the latter
part of 1995 helped to increase the refinery product spread to $3.47 per  barrel
for the full year from just $2.89 per barrel for the first six months.  The 1995
spread  represented  a  9  percent drop from the 1994 level of $3.83 per barrel.
However, throughput volume rose significantly in the second half of the year due
to the improved margins and feedstock mix, resulting in a 10 percent increase in
throughput for full-year 1995.

     The R&M segment benefited  from  key  initiatives to enhance profitability.
The vacuum tower that went into operation in December 1994 raised  the  refinery
product  spread  approximately $.80 per barrel from what it otherwise would have
been.  The segment also began  to  benefit  from  expansion of its Alaska retail
gasoline market share, which grew from 29 percent  in  1994  to  43  percent  at
year-end  1995,  along with product shipments to the Russian Far East.  A larger
impact from these initiatives is expected in 1996.

     The company's Marine Services segment, which includes operations previously
reported as Oil Field Supply and  Distribution,  was the only business area that
did not achieve significant improvements in its fundamental  performance  during
1995.   This  segment recorded a $4.4 million loss, compared with a loss of $2.3
million in 1994.

     "During the latter part  of  1995,  we  initiated a restructuring that will
refocus these operations, including the sale or closure  of  unprofitable  sites
and the merger of the remaining assets with Coastwide Energy Services into a new
Marine  Services  segment, which we expect to complete in February," Smith said.
"This newly consolidated segment should achieve  a strong market share along the
western Gulf Coast, with considerable efficiencies, resulting in a lean and very
profitable business."

     For the fourth quarter of 1995, earnings applicable to  common  stock  were
$8.6 million, or $.35 per share, compared with $15.3 million, or $.61 per share,
in  the  1994 quarter.  The 1995 fourth quarter results were negatively impacted
by a non-cash extraordinary charge of  $2.9  million for the early retirement of
debt, while the  1994  quarter  benefited  from  an  $8.5  million  refund  from
settlement  of an R&M tariff issue, partially offset by charges of approximately
$4  million  related   to   environmental   contingencies   and  other  matters.
Fourth-quarter operating profit was $20.6 million, compared with  $27.3  million
in  the  1994 quarter.  In addition to the tariff issue, the 1994 fourth-quarter
operating results benefited from  Tennessee  Gas  Pipeline Company's election to
take higher volumes of gas under its contract  to  make  up  for  reduced  takes
during 1994's third quarter.

     Tesoro  Petroleum  Corporation  is  a  natural  resource company engaged in
natural gas exploration and  production,  petroleum  refining and marketing, and
wholesale marketing of fuel and lubricants.

                                      -30-


                                    TESORO PETROLEUM CORPORATION
                                    FINANCIAL AND OPERATING DATA
                                     (CONDENSED AND UNAUDITED)
                               (In millions except per unit amounts)


                                                          Three Months Ended         Years Ended
                                                              December 31,           December 31,
                                                          ------------------     ------------------
                                                            1995       1994        1995       1994
                                                                                
BUSINESS SEGMENT DATA
Gross Operating Revenues
 Refining and Marketing:
  Refined products . . . . . . . . . . . . . . . . . .   $  164.9      151.9       664.5      582.7
  Other, including crude oil resales and merchandise .       17.4       11.5       106.5      104.3
 Exploration and Production:
  U.S. oil and gas <F1>. . . . . . . . . . . . . . . .       23.8       31.6       107.3       87.5
  U.S. gas transportation <F1> . . . . . . . . . . . .        1.5        1.2         5.7        3.1
  Bolivia. . . . . . . . . . . . . . . . . . . . . . .        2.6        3.1        11.7       13.2
 Marine Services . . . . . . . . . . . . . . . . . . .       17.6       19.5        74.5       77.9
                                                          --------   --------    --------   --------
  Total Gross Operating Revenues . . . . . . . . . . .   $  227.8      218.8       970.2      868.7
                                                          ========   ========    ========   ========

Summary of Operations
 Segment Operating Profit (Loss):
  Refining and Marketing . . . . . . . . . . . . . . .   $    5.2        6.1          .7        2.4
  Exploration and Production:
   U.S. oil and gas<F2>. . . . . . . . . . . . . . . .       14.6       18.6        96.9       52.1
   U.S. gas transportation . . . . . . . . . . . . . .        1.3        1.2         5.1        2.9
   Bolivia . . . . . . . . . . . . . . . . . . . . . .        1.4        1.9         7.6        9.3
  Marine Services. . . . . . . . . . . . . . . . . . .    (   1.9)  (     .5)    (   4.4)   (   2.3)
                                                          --------   --------    --------   --------
   Total Segment Operating Profit. . . . . . . . . . .       20.6       27.3       105.9       64.4
 Corporate and Unallocated Costs:
  General and administrative expenses. . . . . . . . .        4.0        4.2        16.4       14.7
  Interest expense . . . . . . . . . . . . . . . . . .        4.8        4.7        20.9       18.7
  Interest income  . . . . . . . . . . . . . . . . . .    (   1.2)  (     .9)    (   1.8)   (   2.5)
  Other  . . . . . . . . . . . .                               .9        2.0         8.5        7.4
                                                          --------   --------    --------   --------
 Earnings Before Income Taxes and Extraordinary Item .       12.1       17.3        61.9       26.1
 Income Tax Provision. . . . . . . . . . . . . . . . .         .6        2.0         4.4        5.6
                                                          --------   --------    --------   --------
 Earnings Before Extraordinary Item  . . . . . . . . .       11.5       15.3        57.5       20.5
 Extraordinary Loss on Extinguishment of Debt. . . . .    (   2.9)        -      (   2.9)   (   4.8)
                                                          --------   --------    --------   --------
 Net Earnings. . . . . . . . . . . . . . . . . . . . .        8.6       15.3        54.6       15.7
 Dividend Requirements on Preferred Stock. . . . . . .         -          -           -         2.7
                                                          --------   --------    --------   --------
 Net Earnings Applicable to Common Stock . . . . . . .   $    8.6       15.3        54.6       13.0
                                                          ========   ========    ========   ========

Average Outstanding Common & Common
 Equivalent Shares . . . . . . . . . . . . . . . . . .       25.0       25.0        25.1       23.2
                                                          ========   ========    ========   ========

Earnings Per Share
 Earnings Before Extraordinary Item. . . . . . . . . .   $    .46        .61        2.29        .77
 Extraordinary Loss on Extinguishment of Debt. . . . .    (   .11)        -      (   .11)    (  .21)
                                                          --------   --------    --------   --------
 Net Earnings  . . . . . . . . . . . . . . . . . . . .   $    .35        .61        2.18        .56
                                                          ========   ========    ========   ========

Depreciation, Depletion and Amortization
 Refining and Marketing  . . . . . . . . . . . . . . .   $    3.1        2.6        11.9       10.4
 Exploration and Production:
  U.S. oil and gas . . . . . . . . . . . . . . . . . .        6.2        9.1        29.0       24.1
  U.S. gas transportation. . . . . . . . . . . . . . .         .1         .1          .3         .2
  Bolivia. . . . . . . . . . . . . . . . . . . . . . .         .3         -           .3         -
 Marine Services and Other . . . . . . . . . . . . . .         .1         .3         1.1        1.3
                                                          --------   --------    --------   --------
  Total Depreciation, Depletion and Amortization . . .   $    9.8       12.1        42.6       36.0
                                                          ========   ========    ========   ========

Capital Expenditures
 Refining and Marketing  . . . . . . . . . . . . . . .   $    2.1        9.1         9.3       32.0
 Exploration and Production:
  U.S. oil and gas . . . . . . . . . . . . . . . . . .        8.7       16.7        49.4       60.4
  U.S. gas transportation. . . . . . . . . . . . . . .         .1         .1          .2        5.2
  Bolivia. . . . . . . . . . . . . . . . . . . . . . .        3.8         -          3.8         -
 Marine Services and Other . . . . . . . . . . . . . .         .3         .4         1.2        2.0
                                                          --------   --------    --------   --------
  Total Capital Expenditures . . . . . . . . . . . . .   $   15.0       26.3        63.9       99.6
                                                          ========   ========    ========   ========

REFINING AND MARKETING
Refinery Throughput:
 Barrels per day . . . . . . . . . . . . . . . . . . .     52,092     49,775      50,569     46,032
 % Alaska North Slope crude oil. . . . . . . . . . . .        65%        60%         68%        59%

Refinery Production (Bbls/day):
 Gasoline. . . . . . . . . . . . . . . . . . . . . . .     14,385     13,306      14,298     11,728
 Middle distillates. . . . . . . . . . . . . . . . . .     22,151     19,489      21,140     18,839
 Heavy oils and residual product . . . . . . . . . . .     15,222     16,615      14,516     15,118
 Refinery fuel . . . . . . . . . . . . . . . . . . . .      1,785      1,846       2,042      1,776
                                                          --------   --------    --------   --------
  Total Refinery Production  . . . . . . . . . . . . .     53,543     51,256      51,996     47,461
                                                          ========   ========    ========   ========

Refinery Operations - Product Spread ($/Bbl):
 Yield value of products manufactured -
  Gasoline . . . . . . . . . . . . . . . . . . . . . .   $  25.46      27.91       25.39      25.88
  Middle distillates . . . . . . . . . . . . . . . . .   $  25.33      25.20       24.13      23.94
  Heavy oils and residual product. . . . . . . . . . .   $   9.41       9.01        9.37       8.23
 Average yield value of products manufactured. . . . .   $  20.89      20.72       20.35      19.48
 Cost of raw materials . . . . . . . . . . . . . . . .      16.15      16.38       16.88      15.65
                                                          --------   --------    --------   --------
  Product Spread. . . . . . . . .. . . . . . . . . . .       4.74       4.34        3.47       3.83
 Operating costs. . . . . . . . .. . . . . . . . . . .       2.52       2.69        2.55       2.61
 Depreciation . . . . . . . . . .. . . . . . . . . . .        .50        .45         .51        .45
                                                          --------   --------    --------   --------
  Net Refinery Margin . . . . . .. . . . . . . . . . .   $   1.72       1.20         .41        .77
                                                          ========   ========    ========   ========

Total Product Sales (Bbls/day):
 Gasoline. . . . . . . . . . . . . . . . . . . . . . .     21,451     21,970      24,526     23,191
 Middle distillates. . . . . . . . . . . . . . . . . .     37,085     33,131      37,988     33,256
 Heavy oils and residual product . . . . . . . . . . .     15,737     14,311      14,787     14,228
                                                          --------   --------    --------   --------
  Total Product Sales Volumes. . . . . . . . . . . . .     74,273     69,412      77,301     70,675
                                                          ========   ========    ========   ========

Gross Margin - Merchandise & Other ($ millions). . . .   $    3.0        3.4        12.3       13.1
                                                          ========   ========    ========   ========

EXPLORATION AND PRODUCTION
United States
 Natural Gas production, net (Mcf/day):
  Spot market and other. . . . . . . . . . . . . . . .     82,929     90,009      94,668     65,841
  Tennessee Gas contract <F3>. . . . . . . . . . . . .     15,367     26,353      19,822     17,955
                                                          --------   --------    --------   --------
      Total Production . . . . . . . . . . . . . . . .     98,296    116,362     114,490     83,796
                                                          ========   ========    ========   ========

 Average natural gas sales price ($/Mcf)<F1>:
  Spot market <F4> . . . . . . . . . . . . . . . . . .   $   1.51       1.43        1.34       1.48
  Tennessee Gas contract <F3>. . . . . . . . . . . . .   $   8.64       8.13        8.41       7.93
  Average. . . . . . . . . . . . . . . . . . . . . . .   $   2.63       2.94        2.57       2.86

 Production cost ($/Mcf)<F1> . . . . . . . . . . . . .   $    .25        .28         .29        .29
 Total operating expense ($/Mcf) . . . . . . . . . . .   $    .32        .36         .35        .37
 Depletion ($/Mcf) . . . . . . . . . . . . . . . . . .   $    .69        .85         .69        .79

Bolivia
 Natural gas:
  Production, net (Mcf/day). . . . . . . . . . . . . .     17,388     21,551      18,650     22,082
  Sales price ($/Mcf). . . . . . . . . . . . . . . . .   $   1.25       1.14        1.28       1.20

 Crude oil (condensate):
  Production, net (Bbls/day) . . . . . . . . . . . . .        503        702         567        733
  Sales price ($/Bbl). . . . . . . . . . . . . . . . .   $  14.22      13.67       14.39      13.28

 Production cost ($/NeMcf) . . . . . . . . . . . . . .   $    .07        .07         .07        .06
 Total operating expense ($/NeMcf) . . . . . . . . . .   $    .56        .50         .48        .41

EBITDA, CONSOLIDATED<F5> ($ millions) . . . . . . . . .  $   26.7       34.1       125.4       80.8

<FN>
<F1>   Amounts previously reported have been changed to conform with the current presentation.
<F2>   Operating profit from the Exploration and Production  segment for the year ended December 31,
       1995 included a gain of approximately $33 million from the sale of certain interests  in  the
       Bob West Field.

<F3>   As previously disclosed, the Company is involved in litigation with Tennessee Gas Pipeline Company.
<F4>   Includes  effects  of  the Company's natural gas price swaps which amounted to a gain of $.01
       per Mcf for both the 1995 and 1994 years and a  loss of $.09 per Mcf and gain of $.03 per Mcf
       for the three months ended December 31, 1995 and 1994, respectively.
<F5>   EBITDA represents earnings  before  extraordinary  loss,  interest  expense, income taxes and
       depreciation, depletion and amortization.   EDITDA,  while  not  purporting  to  reflect  any
       measure of the Company's operations or cash flow, is presented for additional analysis.