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


                             TESORO'S RESERVES AND
                         1996 CAPITAL BUDGET ANNOUNCED

     San Antonio,  Texas  --  Jan.  30,  1996  --  Tesoro  Petroleum Corporation
(NYSE:TSO) today announced its Exploration  &  Production  (E&P)  segment  added
natural  gas  reserves  at  about double its total production level during 1995,
although year-end proved reserves were lower due to property sales.  The company
also announced its 1996 capital budget, the bulk of which is directed at E&P.

     In 1995, Tesoro added  96  billion  cubic  feet-equivalent (Bcfe) of proved
reserves, virtually all of  which  were  natural  gas  in  south  Texas.   These
additions,  including  revisions  of  prior  estimates,  replaced 193 percent of
overall net production of 49.8 Bcfe,  of  which 8 Bcfe were produced in Bolivia.
Focusing on Tesoro's south Texas operations, the company replaced 230 percent of
net  domestic  production,  which  totaled  41.8  Bcfe  during  1995.    Without
revisions, Tesoro added 50.2 Bcfe of domestic proved reserves, for a 120 percent
domestic replacement rate.

     Tesoro's  domestic  proved  reserve  additions in 1995 were achieved at low
cost,  bringing  its  three-year  finding   cost  to  $.70  per  thousand  cubic
feet-equivalent, which is among the lowest in  the  industry.   These  additions
were  realized  with  an  85 percent domestic drilling-success rate during 1995,
reflecting 100 percent success on 17 development wells (9.71 net) and 56 percent
success on nine exploratory wells (3.63 net).

     For the year, Tesoro's net proved domestic reserves declined 18 percent due
to the recent sale  of  certain  Bob  West  field interests, which accounted for
approximately 77 Bcfe of net proved reserves.  Tesoro ended the year with  106.4
Bcfe of domestic net proved reserves, compared with 129.1 Bcfe at year-end 1994.

     "Our  domestic  drilling  program  had  a very successful year," Tesoro E&P
President Robert Oliver said.  "Even  though we sold properties containing about
77 Bcfe and produced about 42 Bcfe, our year-end  domestic  reserves  were  down
less than 23 Bcfe.  Looking ahead, we expect to derive significant benefits from
the  recent  sale  of  some of our Bob West field interests.  Aside from greatly
strengthening our financial position, proceeds from  the sale are enabling us to
move forward with

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high-potential  drilling opportunities outside the Bob West field.  During 1995,
on a minimal exploration budget of less than $8 million, we participated in nine
exploratory wells in other parts of south Texas, with a 56 percent success rate.
Included in these numbers is  our  Longoria  No.1 well, which represents a major
new discovery that we named the Tea Jay field.  We  expect  to  accelerate  this
domestic drilling program in 1996."

     Oliver  noted  that  potentially major enhancements also are on the horizon
for Tesoro's Bolivian operations.  Passage of a new hydrocarbons law in Bolivia,
expected by mid-year,  would  significantly  boost  Tesoro's proved reserves due
solely to a resulting extension of the company's  contracts  of  operation.   In
addition,  proposed  pipeline  projects  in the region are moving forward, which
would open up significant new markets for Tesoro's production.

     "We have discovered five fields on  our 1.3 million acres under contract in
Bolivia, with another prospect currently drilling," Oliver said.  "Two of  these
fields are shut in and the other three could produce at much higher levels if we
had access to sufficient markets.  We fully expect our Bolivian operations to go
from being a static asset to a very dynamic asset within the next few years."

     Tesoro completed one well (.73 net) in Bolivia during 1995, discovering the
new Palo Marcado natural gas field, which has estimated gross potential reserves
of  more  than 250 Bcfe.  However, until the new hydrocarbon law is approved and
the contracts are  extended,  no  proved  reserves  can  be attributable to this
success.  As a result, Tesoro's Bolivian reserves fell 8 percent  to  98.0  Bcfe
from year-end 1994.

                              Capital Expenditures
     Tesoro  plans  company-wide  1996 capital expenditures of approximately $51
million, compared with $64 million in 1995.  The E&P segment accounts for almost
$41 million, or 80  percent,  of  the  budgeted  expenditures, compared with $53
million, or 84 percent, in 1995.  Spending for  Tesoro's  Refining  &  Marketing
(R&M) segment in 1996 is expected to be approximately $9 million, about the same
as in 1995.

     The  E&P  segment's  1995  capital  expenditures  included  $49 million for
domestic operations and $4 million  in  Bolivia.   The 1996 E&P budget calls for
$36 million of domestic expenditures and approximately $5  million  in  Bolivia,
where  the current drilling program includes two exploratory

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wells,  one of which is now drilling.  Planned domestic expenditures include $21
million for exploration, development and acquisition outside the Bob West field,
reflecting a 100 percent increase.  Expenditures for Bob West field development,
on the other hand, are budgeted at  $15  million, down from about $39 million in
1995.  Tesoro expects to substantially complete its development  of  this  field
during 1996.

     "Our drilling focus has definitely shifted away  from  the  development  of
this  one field, which accounted for 80 percent of domestic E&P capital spending
in 1995  but  only  40  percent  of  planned  1996  expenditures,"  Oliver said.
"However, we plan to remain in the same general area of south Texas  within  the
Wilcox  trend, capitalizing on the expertise we've developed in the region.  The
outstanding exploratory success  we  recorded  during  1995  gives us additional
confidence in the drilling prospects we have targeted for 1996."

     Approximately 15 percent of the  R&M  segment's  $9  million  1996  capital
budget  is  earmarked  for  the  installation  of facilities that will allow the
company to begin producing and  marketing  asphalt in Alaska, where Tesoro hopes
to capture a 20 percent market share by year-end.  The remainder of the  planned
expenditures  is  targeted primarily toward maintenance and upgrades at Tesoro's
refinery and 7-Eleven convenience stores in Alaska, roughly the same as in 1995.

     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.

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