EXHIBIT 24


                                POWER OF ATTORNEY

         Each person whose signature appears below constitutes and appoints
Michael W. J. Smurfit, Roger W. Stone, and Patrick J. Moore, and each of them,
his true and lawful attorney-in-fact and agent, with full power of substitution
and resubstitution, for him and in his name, place and stead, in any and all
capacities, to sign Annual Reports on Form 10-K and all required interim reports
and to file the same, with all exhibits thereto, and other documents in
connection therewith, regarding Stone Container Corporation, a Delaware
corporation, with the Securities and Exchange Commission and any other
regulatory authority, granting unto said attorney-in-fact and agents, 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 as he might or could do in person, hereby ratifying and confirming all
that said attorneys-in-fact and agents, or their substitutes, may lawfully do or
cause to be done by virtue hereof.

     Signature                                Title
     ---------                                -----

/s/ Roger W. Stone                     President, Chief Executive
- -------------------                    Officer and Director       
    Roger W. Stone                     (Principal Executive Officer)


/s/ Raymond M. Curran                  Executive Vice President and 
- ----------------------                 Deputy Chief Executive Officer
     Raymond M. Curran                 Officer and Director


/s/ Patrick J. Moore                   Vice President and Chief Financial 
- ---------------------                  Officer
     Patrick J. Moore                  (Principal Accounting Officer and
                                       Principal Financial Officer)


/s/ David Gale                         Director
- ---------------                                
     David Gale


/s/ Mark A. Weissman                   Director
- ---------------------                          
     Mark A. Weissman



Date:  February 11, 1999