1
                                                                    EXHIBIT 23.1


                       Consent of Independent Accountant

We hereby consent to the incorporation by reference in the Prospectus
constituting part of the Registration Statement on Form S-3 (No. 333-51789) of
Tesoro Petroleum Corporation of our report dated May 29, 1998 relating to the
financial statements of Shell Anacortes Refining Company, which appears in the
Current Report on Form 8-K of Tesoro Petroleum Corporation dated June 5, 1998.
We also consent to the reference to us under the heading "Experts" in the two
Prospectus Supplements for the Common Stock and Premium Income Equity Securities
Offerings, which are a part of such Registration Statement.


/s/ PRICE WATERHOUSE LLP
Price Waterhouse LLP
Houston, Texas
June 5, 1998