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                                                                     EXHIBIT 5.1

                                August 26, 1997


Halliburton Company
3600 Lincoln Plaza
500 North Akard Street
Dallas, Texas 75201-3391

Ladies and Gentlemen:

     We acted as counsel for Halliburton Company, a Delaware corporation 
("Halliburton"), in connection with Halliburton's Form S-4 registration 
statement (the "Registration Statement") relating to the offering, issuance and 
sale of shares (the "Shares") of Halliburton's common stock, par value $2.50 per
share, pursuant to the proposed merger of Halliburton M.S. Corp., a Delaware 
corporation and wholly owned subsidiary of Halliburton, with and into NUMAR 
Corporation, a Pennsylvania corporation.

     Before rendering our opinion, we examined certain of the corporate records 
of Halliburton, including its Restated Certificate of Incorporation (as 
amended), certain resolutions of the Board of Directors of Halliburton, the 
Registration Statement and the exhibits thereto and such certificates of 
corporate officers of Halliburton and governmental officials as we deemed 
necessary for the purposes of this opinion. As to matters of fact relevant to 
the opinions expressed herein, and as to factual matters arising in connection 
with our examination of the above described documents, we relied upon 
certificates and other communications of corporate officers of Halliburton and 
governmental officials without further investigation as to the facts set forth 
therein. We are rendering this opinion as of the effective date of the 
Registration Statement.

     Based upon the foregoing, we are of the opinion that the Shares have been 
validly authorized for issuance and, upon issuance as described in the 
Registration Statement, will be validly issued, fully paid and nonassessable.

     We hereby consent to the filing of this letter as an exhibit to the 
Registration Statement. By giving such consent, we do not admit that we are 
within the category of persons whose consent is required under Section 7 of the 
Securities Act of 1933, as amended, or the rules and regulations of the 
Securities and Exchange Commission issued thereunder. For purposes of the 
foregoing opinions,
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Halliburton Company
Page 2
August 26, 1997

we assumed that the Shares will be offered, issued and sold in compliance with 
all applicable state securities or Blue Sky laws.

                                             Very truly yours,

                                             /s/ VINSON & ELKINS L.L.P.

                                             VINSON & ELKINS L.L.P.

