Exhibit 8.1


(713) 758-2192                                                    (713) 615-5210


                                August 25, 1997


Halliburton Company
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 M.S. Corp. ("Newco"), a Delaware corporation and a
wholly owned subsidiary of Halliburton Company (the "Acquiror"), a Delaware
corporation, with and into NUMAR Corporation (the "Company"), a Pennsylvania
corporation (the "Merger").

     Our opinion is based upon (i) the Agreement and Plan of Merger dated as of
June 9, 1997, by and among the Acquiror, Newco and the Company (the "Merger
Agreement")/1/, including the representations contained therein/2/, (ii) the
facts set forth in the Registration Statement filed with the Securities and
Exchange Commission with respect to the Merger, (iii) the written
representations of officers of the Acquiror and the Company, copies of which are
attached hereto, and (iv) current provisions of the Code, existing regulations
thereunder, current administrative rulings of the Internal Revenue Service and
court decisions. Based thereupon, and conditioned upon our understanding that
the transactions contemplated by the Merger Agreement will be carried out
strictly in accordance with the terms of the Merger Agreement, it is our opinion
that:

          (i)  the Merger will constitute a reorganization under section 368(a) 
     of the Code;


          (ii) the Acquiror, the Company and Newco will each be a party to that 
     reorganization within the meaning of section 368(b) of the Code; and


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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 
Sections 4.18 and 5.16 of the Merger Agreement.

 
Halliburton Company
Page 2
August 25, 1997


        (iii)  no gain or loss will be recognized by the Acquiror, the Company 
     or Newco by reason of the Merger.

     We participated in the preparation of the Registration Statement. We hereby
confirm that the conclusions of law with respect to federal income tax matters 
set forth in the Registration Statement under the heading "Certain Federal 
Income Tax Consequences" are accurate and state the material federal income tax 
consequences of the Merger.

     We hereby consent to the use of our name in the Registration Statement and 
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.


                                                Very truly yours,

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

                                                VINSON & ELKINS L.L.P.


 
                               NUMAR CORPORATION

                                  CERTIFICATE


     In connection with the tax opinions to be rendered by Drinker Biddle &
Reath LLP and Vinson & Elkins L.L.P., respectively, regarding certain federal
income tax consequences of the proposed merger (the "Merger") of Halliburton
M.S. Corp. ("Sub"), a direct, wholly owned subsidiary of Halliburton Company
("Halliburton"), with and into NUMAR Corporation ("NUMAR") pursuant to the
Agreement and Plan of Merger dated as of June 9, 1997 (the "Merger Agreement"),
NUMAR hereby certifies:

     1.   Following the Merger, NUMAR will hold at least 90% of the fair market
          value of the net assets and at least 70% of the fair market value of
          the gross assets held by NUMAR prior to the Merger, including any
          assets used to pay dissenting shareholders or reorganization expenses
          or to make other than regular and normal distributions or redemptions.

     2.   There is no plan or intention by the shareholders of NUMAR who own 5%
          or more of the outstanding shares of NUMAR stock or, to our knowledge,
          other shareholders of NUMAR to sell, exchange or otherwise dispose of
          a number of shares of Halliburton stock received by them in the Merger
          which would result in their owning in the aggregate shares of
          Halliburton stock having a fair market value, as of the date of the
          Merger, of less than 50% of the fair market value of all of the
          formerly outstanding stock of NUMAR as of the same date. For purposes
          of this representation, shares of NUMAR stock exchanged for cash or
          other property, surrendered by dissenters or exchanged for cash in
          lieu of fractional shares of Halliburton stock will be treated as
          outstanding NUMAR stock on the date of the Merger. Moreover, shares of
          NUMAR stock and shares of Halliburton stock held by NUMAR shareholders
          and otherwise sold, redeemed, or disposed of in anticipation of the
          Merger, or subsequent to the Merger pursuant to a plan or intention as
          of the date of the Merger, should also be taken into account in
          connection with this representation.

     3.   Following the Merger, NUMAR will not issue additional shares of its
          stock that would result in Halliburton losing control of NUMAR. As
          used herein, "control" means the direct ownership of stock possessing
          at least 80% of the total combined voting power for the election of
          directors of all classes entitled to vote and at least 80% of the
          total number of shares of each nonvoting class of stock of the
          corporation.

 
     4.   In the Merger, shares of NUMAR stock representing control of NUMAR
          will be exchanged solely for voting stock of Halliburton. For this
          purpose, shares of NUMAR stock exchanged for cash or other property
          originating with Halliburton will be treated as outstanding NUMAR
          stock on the date of the Merger.

     5.   Halliburton, NUMAR, Sub and the shareholders of NUMAR will pay their
          respective expenses, if any, incurred in connection with the
          transaction.

     6.   There is no intercorporate indebtedness existing between Halliburton
          and NUMAR or between Sub and NUMAR that was issued, acquired or will
          be settled at a discount.

     7.   At the time of the Merger, NUMAR will not have outstanding any
          warrants, options, convertible securities, or any other type of right
          pursuant to which any person could acquire stock in NUMAR that, if
          exercised or converted, would affect Halliburton's acquisition or
          retention of control of NUMAR.

     8.   On the date of the Merger the fair market value of the assets of NUMAR
          will exceed the sum of its liabilities, plus the amount of
          liabilities, if any, to which the assets are subject.

     9.   No two parties to the Merger are investment companies as defined in
          Section 368 (a) (2) (F) (iii) or (iv) of the Internal Revenue Code.

     10.  NUMAR is not under the jurisdiction of a court in a case under Title
          11 of the United States Code or a receivership, foreclosure or similar
          proceeding in any federal or state court.

     11.  Shares of NUMAR stock are regularly traded on an established
          securities market. No foreign persons hold 5% or greater of the shares
          of NUMAR stock.

     12.  None of the compensation received by any stockholder-employees of
          NUMAR will be separate consideration for, or allocable to, any of
          their shares of NUMAR stock. None of the shares of Halliburton stock
          received by any stockholder-employees of NUMAR will be separate
          consideration for, or allocable to, any employment agreement. The
          compensation paid to any stockholder-employees of NUMAR will be for
          services actually rendered and will be commensurate with amounts paid
          to third parties bargaining at arm's-length for similar services.

     13.  The procedure set forth in the Merger Agreement providing for cash in
          lieu of fractional shares of Halliburton stock in the Merger is solely
          for the purpose of

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          avoiding the expense and inconvenience to Halliburton of issuing
          fractional shares of Halliburton stock and does not represent
          separately bargained-for consideration.

     14.  The Merger Agreement and the documents referred to therein represent
          the full and complete agreement among Halliburton, Sub, and NUMAR
          regarding the Merger, and there are no other written or oral
          agreements regarding the Merger.

     NUMAR understands that (i) each of Drinker Biddle & Reath LLP and Vinson &
Elkins L.L.P. will rely upon the above representations in connection with
issuing their respective opinions, (ii) the representations in this Certificate
are made as of the date hereof and as of the effective date of the Merger, and
(iii) each of Drinker Biddle & Reath LLP and Vinson & Elkins L.L.P. may disclose
these representations in connection with issuing their respective opinions.


     IN WITNESS WHEREOF, NUMAR has caused this Certificate to be signed on its
behalf as of August 25, 1997.


                                         NUMAR CORPORATION



                                         By:  /s/ EDWARD P. DELSON
                                             _________________________________
                                             Name:  Edward P. Delson
                                             Title: Senior Vice President--
                                                    Finance and Administration,
                                                    Chief Financial Officer
                                                    and Treasurer

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                              HALLIBURTON COMPANY

                                  CERTIFICATE


     In connection with the tax opinions to be rendered by Drinker Biddle &
Reath LLP and Vinson & Elkins L.L.P., respectively, regarding certain federal
income tax consequences of the proposed merger (the "Merger") of Halliburton
M.S. Corp. ("Sub"), a direct, wholly owned subsidiary of Halliburton Company
("Halliburton"), with and into NUMAR Corporation ("NUMAR") pursuant to the
Agreement and Plan of Merger dated as of June 9, 1997 (the "Merger Agreement"),
Halliburton, on behalf of itself and Sub, hereby certifies:

     1.  Prior to the Merger, Halliburton will own all the outstanding shares of
         Sub stock and will be in control of Sub. As used herein, "control"
         means the direct ownership of stock possessing at least 80 percent of
         the total combined voting power for the election of directors of all
         classes entitled to vote and at least 80 percent of the total number of
         shares of each nonvoting class of stock of the corporation.

     2.  Halliburton has no plan or intention to reacquire any of the shares of
         Halliburton stock issued in the Merger.

     3.  There is no intercorporate indebtedness existing between Halliburton
         and NUMAR or between Sub and NUMAR that was issued, acquired or will be
         settled at a discount.

     4.  Halliburton has no plan or intention to liquidate NUMAR; to merge NUMAR
         with or into another corporation; to sell or otherwise dispose of the
         stock of NUMAR except for transfers of stock to corporations controlled
         by Halliburton; or to cause NUMAR to sell or otherwise dispose of any
         of its assets, or of any of the assets of Sub acquired in the Merger,
         except for dispositions made in the ordinary course of business or
         transfers to a corporation controlled by NUMAR.

     5.  In the Merger, Sub will have no liabilities assumed by NUMAR, and will
         not transfer to NUMAR any assets subject to liabilities.

     6.  Following the Merger, NUMAR will continue its historic business or use
         a significant portion of its historic business assets in a business.

     7.  Halliburton, NUMAR, Sub and the shareholders of NUMAR will pay their
         respective expenses, if any, incurred in connection with the 
         transaction.

 
     8.   No two parties to the Merger are investment companies as defined in
          Section 368 (a) (2) (F) (iii) and (iv) of the Internal Revenue Code.

     9.   The fair market value of the Halliburton stock and any other
          consideration received by each NUMAR shareholder will be approximately
          equal to the fair market value of the NUMAR stock surrendered in the
          exchange.

     10.  Halliburton does not own, nor has it owned for the past five years,
          any shares of the stock of NUMAR.

     11.  The procedure set forth in the Merger Agreement providing for cash in
          lieu of fractional shares of Halliburton stock in the Merger is solely
          for the purpose of avoiding the expense and inconvenience to
          Halliburton of issuing fractional shares of Halliburton stock and does
          not represent separately bargained-for consideration.

     12.  The Merger Agreement and the documents referred to therein represent
          the full and complete agreement among Halliburton, Sub, and NUMAR
          regarding the Merger, and there are no other written or oral
          agreements regarding the Merger.

     Halliburton and Sub understand that (i) each of Drinker Biddle & Reath LLP
and Vinson & Elkins L.L.P. will rely upon the above representations in
connection with issuing their respective opinions, (ii) the representations in
this Certificate are made as of the date hereof and as of the effective date of
the Merger, and (iii) each of Drinker Biddle & Reath LLP and Vinson & Elkins
L.L.P. may disclose these representations in connection with issuing their
respective opinions.

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   IN WITNESS WHEREOF, on behalf of Halliburton and Sub, Halliburton has
caused this Certificate to be signed on its behalf as of August 25, 1997.
 

                                          HALLIBURTON COMPANY



                                          By:  /s/ SUSAN S. KEITH
                                              _________________________________
                                              Name:  Susan S. Keith
                                              Title: Vice President and
                                                     Secretary

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