
<PAGE>
 
                                                                    EXHIBIT 24.1


                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 24, 1997        /s/ Anne L. Armstrong
                            ---------------------
                            Anne L. Armstrong
                            Title:  Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints David J. Lesar, Lester
L. Coleman, Gary V. Morris and Susan S. Keith, and each or any of them, his or
her true and lawful attorneys-in-fact and agents (with full power to each of
them to act alone), with full power of substitution and resubstitution for him
or her and in his or her name, place and stead in any and all capacities, to
sign the Registration Statement on Form S-4, or other appropriate Form, relating
to the merger of Halliburton M.S. Corp., a wholly-owned subsidiary of
Halliburton Company, with and into NUMAR Corporation, and any and all amendments
(including post-effective amendments) or supplements to such Registration
Statement, and to file the same, with all exhibits thereto and all documents in
connection therewith, with the Securities and Exchange Commission, granting unto
said attorneys-in-fact and agents full power and authority to do and perform
each and every act and thing requisite and necessary to be done (with full power
to each of them to act alone), as fully and to all intents and purposes as he or
she might or could do in person, hereby ratifying and confirming all that said
attorneys-in-fact and agents or any of them, or their substitutes, may lawfully
do or cause to be done by virtue hereof.

Date:  June 15, 1997        /s/ Richard B. Cheney
                            ---------------------
                            Richard B. Cheney
                            Title:  Chairman of the Board and
                                     Chief Executive Officer and
                                     Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 16, 1997        /s/ Clitheroe
                            -------------
                            Lord Clitheroe
                            Title:  Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 16, 1997        /s/ Robert L. Crandall
                            ----------------------
                            Robert L. Crandall
                            Title:  Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 18, 1997        /s/ W. R. Howell
                            ----------------
                            W. R. Howell
                            Title:  Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 15, 1997        /s/ Dale P. Jones
                            -----------------
                            Dale P. Jones
                            Title:  Vice Chairman and
                                    Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 15, 1997        /s/ Delano E. Lewis
                            -------------------
                            Delano E. Lewis
                            Title:  Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 15, 1997        /s/ C. J. Silas
                            ---------------
                            C. J. Silas
                            Title:  Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 15, 1997        /s/ Roger T. Staubach
                            ---------------------
                            Roger T. Staubach
                            Title:  Director
<PAGE>
 
                               POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints Richard B. Cheney, David
J. Lesar, Lester L. Coleman, Gary V. Morris and Susan S. Keith, and each or any
of them, his or her true and lawful attorneys-in-fact and agents (with full
power to each of them to act alone), with full power of substitution and
resubstitution for him or her and in his or her name, place and stead in any and
all capacities, to sign the Registration Statement on Form S-4, or other
appropriate Form, relating to the merger of Halliburton M.S. Corp., a wholly-
owned subsidiary of Halliburton Company, with and into NUMAR Corporation, and
any and all amendments (including post-effective amendments) or supplements to
such Registration Statement, and to file the same, with all exhibits thereto and
all documents in connection therewith, with the Securities and Exchange
Commission, granting unto said attorneys-in-fact and agents full power and
authority to do and perform each and every act and thing requisite and necessary
to be done (with full power to each of them to act alone), as fully and to all
intents and purposes as he or she might or could do in person, hereby ratifying
and confirming all that said attorneys-in-fact and agents or any of them, or
their substitutes, may lawfully do or cause to be done by virtue hereof.

Date:  June 17, 1997        /s/ R. J. Stegemeier
                            --------------------
                            Richard J. Stegemeier
                            Title:  Director
