EXHIBIT 32

Certification of Principal Executive Officer and Principal Financial Officer
Pursuant to 18 U.S.C. Section 1350, as Adopted Pursuant to Section 906 of the
Sarbanes – Oxley Act of 2002

     The undersigned, who are the chief executive officer and the chief financial officer of Sonoco Products Company, the company sponsor of the Sonoco Savings Plan, each hereby certifies that, to the best of his knowledge, the accompanying Form 11-K for the year ended December 31, 2003, fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in the report fairly presents, in all material respects, the financial condition and results of operations of the Plan.

June 28, 2004

/s/Harris E. DeLoach, Jr.  

Harris E. DeLoach, Jr. 

Chief Executive Officer of Sonoco Products
Company, the company sponsor of the
Sonoco Savings Plan 

/s/Charles J. Hupfer  

Charles J. Hupfer 

Chief Financial Officer of Sonoco Products
Company, the company sponsor of the
Sonoco Savings Plan 

A signed original of this written statement required by Section 906 has been provided to Sonoco Products Company and will be retained by Sonoco Products Company and furnished to the Securities and Exchange Commission upon request. This certification accompanies the Form 11-K and shall not be treated as having been filed as part of the Form 11-K.