1 Exhibit 99.2 NEWS RELEASE FOR IMMEDIATE RELEASE: CONTACT: SUSAN PIROTINA (210) 283-2631 TESORO ANNOUNCES PRIVATE OFFERING OF SENIOR SUBORDINATED NOTES SAN ANTONIO -- JUNE 1, 1998 -- Tesoro Petroleum Corporation (NYSE: TSO) announced today that it plans a private offering of $300 million in Senior Subordinated Notes eligible for Rule 144A in connection with its plans to finance its recent refinery acquisitions. The Company recently completed the acquisition of a refinery and 32 retail marketing outlets in Hawaii from The Broken Hill Proprietary Company Limited and has agreed to acquire a refinery in Anacortes, Washington from Shell Refining Holding Company. In connection with these acquisitions, the Company intends to raise proceeds from certain previously announced public equity offerings and the proposed offering of Senior Subordinated Notes. The Senior Subordinated Notes are expected to have a ten-year maturity without sinking fund requirements. The Notes will be subject to optional redemption by the Company after five years at declining premiums. The Senior Subordinated Notes will not be registered under the Securities Act of 1933, as amended, and may not be offered or sold in the United States absent registration or an applicable exemption from registration requirements. Tesoro Petroleum Corporation is a natural resource company engaged in petroleum refining and marketing, natural gas exploration and production, marketing and distributing petroleum products and providing marine logistics services. -30-