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.