<PAGE>   1
                                                                     Exhibit 24

                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 24th day of March, 1998.
 
                                                   /S/ Samuel B. Davis
                                                   ----------------------------
                                       36
<PAGE>   2
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 23rd day of March, 1998.
 
                                                   /S/ Samuel N. Davis
                                                   ----------------------------
 
                                       37
<PAGE>   3
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 23rd day of March, 1998.
 
                                                   /S/ Robert S. Hamilton
                                                   ----------------------------
 
                                        38
<PAGE>   4
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 24th day of March, 1998.
 
                                                   /S/ Charles R. Coate
                                                   ----------------------------
 
                                        39
<PAGE>   5
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 27th day of March, 1998.

                                                   /S/ C. William McBee
                                                   ----------------------------
 
                                       40
<PAGE>   6
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 26th day of March, 1998.
 
                                                   /S/ Carl J. Aschinger, Jr.
                                                   ----------------------------

                                       41
<PAGE>   7
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 23rd day of March, 1998.
 
                                                   /S/ Russell M. Gertmenian
                                                   ----------------------------

                                       42
<PAGE>   8
 
                               POWER OF ATTORNEY
 
     KNOW ALL MEN BY THESE PRESENTS, that the undersigned officer and/or
director of LIQUI-BOX CORPORATION, an Ohio corporation, which is about to file
with the Securities and Exchange Commission, Washington, D. C., under the
provisions of the Securities Exchange Act of 1934, as amended, an Annual Report
on Form 10-K, hereby constitutes and appoints Samuel B. Davis, C. William McBee,
and James B. Holloway his/her true and lawful attorneys-in-fact and agents, with
full power of substitution and resubstitution, for him/her and in his/her name,
place and stead, in any and all capacities, to sign such Report and any or all
amendments or documents related thereto, and to file the same, with all exhibits
thereto, and other documents in connection therewith, with the Securities and
Exchange Commission, granting unto said attorneys-in-fact and agents, and
substitute or substitutes, and each of them, full power and authority to do and
perform each and every act and thing requisite and necessary to be done in and
about the premises, as fully to all intents and purposes and he/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 or his/her substitute or
substitutes may lawfully do or cause to be done by virtue hereof.
 
IN WITNESS WHEREOF, the undersigned has hereunto set his/her hand and seal as of
this 20th day of March, 1998.
 
                                                   /S/ James B. Holloway
                                                   ----------------------------

                                       43