Exhibit 8.1

                     [Letterhead of Vinson & Elkins L.L.P.]

                                                                   July 17, 2001

Dresser Industries, Inc.
3600 Lincoln Plaza
500 North Akard Street
Dallas, Texas 75201-3391

Ladies and Gentlemen:

   You have requested our opinion with respect to certain federal income tax
consequences under the Internal Revenue Code of 1986, as amended (the "Code")
of the merger of Halliburton MS, Inc. ("Merger Sub"), a Delaware corporation
and a direct, wholly-owned subsidiary of Dresser Industries, Inc. ("Dresser"),
a Delaware corporation and a direct, wholly-owned subsidiary of Halliburton
Company, a Delaware corporation, with and into Magic Earth, Inc. (the
"Company"), a Delaware corporation (the "Merger").

   Our opinion is based upon (i) the Agreement and Plan of Merger dated as of
April 29, 2001 by and among Halliburton, Dresser, Merger Sub, the Company and
certain of the Company's stockholders (the "Merger Agreement")/1/ , (ii) the
facts set forth in the Registration Statement filed with the Securities and
Exchange Commission with respect to the Merger (the "Registration Statement"),
(iii) officers' certificates containing representations and certifications made
to us by Dresser and the Company/2/, and (iv) current provisions of the Code,
existing regulations thereunder, current administrative rulings of the Internal
Revenue Service and court decisions.

   In our opinion, the Merger will be treated for federal income tax purposes
as a reorganization qualifying under section 368(a) of the Code, and Dresser,
Halliburton and the Company will each be a party to that reorganization within
the meaning of section 368(b) of the Code. Accordingly, no gain or loss will be
recognized by Dresser, Halliburton, the Company or Merger Sub by reason of the
Merger. Further, (i) no gain or loss will be recognized by a stockholder of the
Company upon the receipt of Halliburton Common Stock in exchange for Company
Common Stock except with respect to any cash received in lieu of a fractional
share of Halliburton Common Stock, (ii) the aggregate tax basis of the shares
of Halliburton Common Stock received by a stockholder of the Company in the
Merger (including any fractional share deemed received) will be the same as the
aggregate tax basis of the shares of Company Common Stock surrendered in
exchange therefor, (iii) the holding period of the shares of Halliburton Common
Stock received by a stockholder of the Company
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/1/Capitalized terms used but not defined herein have the meanings ascribed to
  them in the Merger Agreement.
/2/Representations concerning federal tax matters are set forth in the Dresser
  Industries, Inc. Officer's Certificate executed by Lester L. Coleman, Senior
  Vice President of Dresser on July 17, 2001 and the Magic Earth, Inc.
  Officer's Certificate executed by Michael J. Zeitlin, Chairman & Chief
  Executive Officer of the Company on July 17, 2001.


in the Merger (including any fractional share deemed received) will include the
holding period of the shares of Company Common Stock surrendered in exchange
therefor, provided that the shares of Company Common Stock are held as capital
assets at the Effective Time, and (iv) a stockholder of the Company who
receives cash in lieu of a fractional share of Halliburton Common Stock will
recognize gain or loss (which will be capital gain or loss if the Company
Common Stock is held by the stockholder as a capital asset at the Effective
Time) equal to the difference, if any, between the stockholder's tax basis in
the fractional share (as described above) and the amount of cash received.

   This opinion is given to you by us solely for your use and benefit, and is
not to be quoted or otherwise referred to or furnished to any governmental
agency (other than the Securities and Exchange Commission in connection with
the Registration Statement filed with respect to the Merger or the Internal
Revenue Service in connection with an examination of the transactions
contemplated by the Merger Agreement) or to any other person without our prior
written consent.

   We hereby consent to the use of our name in the Registration Statement and
to the filing of this opinion as part of the Registration Statement.


                                          Very truly yours,

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