EXHIBIT 99.1

 
[X] Please mark your     SHARES IN YOUR NAME           
    example.             
                                                                    X
                                                                    X
                                                                    X
                                                                    XXXXXXX
     

                      FOR  AGAINST ABSTAIN
                      [_]    [_]     [_]

                      With respect to the proposal (the "Proposal") to   
                      approve and adopt the Agreement and Plan of Merger, 
                      dated as of June 30, 1996, by and among Halliburton 
                      Company, Halliburton Acq. Company and Landmark, as 
                      described in the accompanying Proxy Statement/Prospectus. 


                                              IMPORTANT: In signing this        
                                              proxy please sign exactly         
                                              as your name(s) is (are)          
                                              shown on the share certificate    
                                              to which this proxy relates.      
                                              When signing as an attorney,      
                                              executor, administrator,          
                                              trustee or guardian, please       
                                              give your full title as such. If a
          Change                              corporation, please sign in full 
     [_]    of                                corporate name and indicate the  
          Address                             capacity of the duly authorized  
                                              officer executing this proxy on  
                                              behalf of the corporation. If a  
                                              partnership, please sign in full 
                                              partnership name and indicate the
                                              capacity of the duly authorized  
                                              person executing this proxy on   
                                              behalf of the partnership. EACH  
                                              JOINT TENANT MUST SIGN.          
 
        SIGNATURE(S)                                 DATE     
                   ------------------------------       -------


        SIGNATURE(S)                                 DATE
                    ------------------------------       -------
   PLEASE SIGN, DATE AND RETURN YOUR PROXY PROMPTLY IN THE ENVELOPE PROVIDED,
WHICH REQUIRES NO POSTAGE IF MAILED IN THE UNITED STATES.
- --------------------------------------------------------------------------------

                   PROXY FOR SPECIAL MEETING OF STOCKHOLDERS
 
                         LANDMARK GRAPHICS CORPORATION
                              15150 MEMORIAL DRIVE
                           HOUSTON, TEXAS 77079-4304
 
          THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS
 
  The undersigned stockholder hereby appoints Robert P. Peebler and Patti L.
Massaro, or either of them, as proxies, each with full powers of substitution,
and hereby authorizes them to represent and to vote, as designated below, all
shares of Common Stock, par value $.05 per share, of Landmark Graphics
Corporation, a Delaware corporation ("Landmark"), held of record by the
undersigned on the Record Date (as defined in the accompanying Proxy
Statement/Prospectus) at the Special Meeting (as defined in the accompanying
Proxy Statement/Prospectus), and at any adjournment or postponement thereof and
hereby revokes any prior proxy granted with respect thereto.
 
  This proxy, when properly executed and returned in a timely manner, will be
voted at the Special Meeting and any adjournment or postponement thereof in the
manner described herein. IF NO CONTRARY INDICATION IS MADE, THIS PROXY WILL BE
VOTED FOR THE PROPOSAL (AS HEREINAFTER DEFINED).
 
  THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS OF LANDMARK. THE
BOARD OF DIRECTORS UNANIMOUSLY RECOMMENDS THAT YOU VOTE FOR THE PROPOSAL.
 
  Each of the above named proxies present at the Special Meeting, either in
person or by substitute, shall have and exercise all the powers of said proxies
hereunder. This proxy will be voted in accordance with the choice specified by
the undersigned on this proxy or, if no choice is made, FOR the Proposal. In
their discretion, each of the above-named proxies is authorized to vote upon
such other business incident to the conduct of the Special Meeting as may
properly come before the Special Meeting or any postponements or adjournments
thereof.
 
  The undersigned acknowledges receipt of a copy of the Notice of Special
Meeting of Stockholders and the Proxy Statement/Prospectus relating to the
Special Meeting.
 
                  (CONTINUED AND TO BE SIGNED ON REVERSE SIDE)