EXHIBIT 5.1 VINSON & ELKINS ATTORNEYS AT LAW VINSON & ELKINS L.L.P. 1001 FANNIN STREET SUITE 2300 HOUSTON, TEXAS 77002-6760 TELEPHONE (713) 758-2222 FAX (713) 758-2346 WRITER'S TELEPHONE WRITER'S FAX (713) 758-1074 (713) 615-5926 August 30, 1996 Halliburton Company 3600 Lincoln Plaza 500 North Akard Street Dallas, Texas 75201-3391 Ladies and Gentlemen: We acted as counsel to Halliburton Company, a Delaware corporation (the "Company"), in connection with the preparation of the Company's Registration Statement on Form S-4 as filed with the Securities and Exchange Commission (the "Commission") on the date hereof (the "Registration Statement") pursuant to the Securities Act of 1933, as amended (the "Act"), which Registration Statement relates to the proposed issuance by the Company of certain shares of the Company's Common Stock, par value $2.50 per share ("Common Stock"), in accordance with the Agreement and Plan of Merger (the "Merger Agreement") dated as of June 30, 1996, among the Company, Landmark Graphics Corporation ("Landmark") and Halliburton Acq. Company, which Merger Agreement provides for the acquisition by the Company of Landmark by means of the merger described therein (the "Merger"). In such connection, we are passing on certain legal matters in connection with the foregoing issuance of Common Stock. At your request, this opinion is being furnished to you for filing as an exhibit to the Registration Statement. Before rendering this opinion, we examined such certificates, instruments and documents and reviewed such questions of law as we considered necessary or appropriate. In addition, we relied as to factual matters on certificates of certain public officials and officers of the Company. Based upon the foregoing examination and review, we are of the opinion that the shares of Common Stock to be issued pursuant to the Merger (i) have been duly authorized and (ii) when the conditions to the Merger set forth in the Merger Agreement have been satisfied (including the condition that the Registration Statement has become effective under the Act) and the Merger has been effected in accordance therewith, will be validly issued, fully paid and non-assessable shares of Common Stock. We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the references to our firm under the caption "Legal Matters" in the Proxy Statement/ Prospectus forming a part of the Registration Statement. In giving this consent, however, we do not HOUSTON DALLAS WASHINGTON, D.C. AUSTIN MOSCOW LONDON MEXICO CITY SINGAPORE Halliburton Company Page 2 August 30, 1996 hereby admit that we are within the category of persons whose consent is required under Section 7 of the Act and the rules and regulations of the Commission thereunder. Very truly yours, VINSON & ELKINS L.L.P.