<PAGE>   1

                                                                     EXHIBIT 3.1


                               State of Delaware
                                        
                        Office of the Secretary of State       Page 1
                        --------------------------------


     
     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY
CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF LIMITED
PARTNERSHIP OF "SOUTHERN FOODS GROUP, L.P.", FILED IN THIS OFFICE ON THE
TWENTIETH DAY OF DECEMBER, A.D. 1994, AT 11:30 O'CLOCK A.M.

                     



                     [GREAT SEAL OF THE STATE OF DELAWARE]



                                             /s/ EDWARD J. FREEL
                               [SEAL]        -----------------------------------
                                             Edward J. Freel, Secretary of State
                                                                                
2463482  8100                                AUTHENTICATION: 8919228
                                                                                
981056958                                    DATE: 02-12-98





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                                                           STATE OF DELAWARE
                                                          SECRETARY OF STATE
                                                      DIVISION OF CORPORATIONS
                                                     FILED 11:30 AM 12/20/1994
                                                         944250818 - 2463482


                       CERTIFICATE OF LIMITED PARTNERSHIP

                                       OF

                           SOUTHERN FOODS GROUP, L.P.



     THE UNDERSIGNED, desiring to form a limited partnership under the laws of
the State of Delaware, does hereby certify as follows:

     1.   The name of the limited partnership is Southern Foods Group, L.P.
          (the "Partnership").

     2.   The registered office of the Partnership in the State of Delaware is
          located at 1209 Orange Street, City of Wilmington, County of New 
          Castle, 19801. The name of the registered agent at such address is The
          Corporation Trust Company.

     3.   SFG Management Limited Liability Company, a Delaware limited
          liability company (the "General Partner"), is the sole general partner
          of the Partnership. The business address of the General Partner is 
          3114 South Haskell, Dallas, Texas 75223.

     IN WITNESS WHEREOF, the undersigned has executed this Certificate as of
this 19th day of December, 1994.


                                                SFG MANAGEMENT LIMITED LIABILITY
                                                COMPANY, as sole General Partner
                                                                                
                                                                                
                                                By:  /s/ F.T. SCHENKEL
                             [SEAL]                -----------------------------
                                                    F.T. Schenkel, President