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