EXHIBIT 13.(a).1

                            CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350,
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

     In connection with the Annual Report of Tefron Ltd. (the "Company") on Form
20-F for the period ending December 31, 2004, as filed with the Securities and
Exchange Commission on the date hereof (the "Report"), the undersigned hereby
certify that to the best of our knowledge:

     1. The Report fully complies with the requirements of Section 13(a) or
15(d) of the Securities Exchange Act of 1934; and

     2. The information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of the Company.

Date: April 19, 2005
                                                  /s/ Yosef Shiran
                                                  ----------------
                                                  Name:  Yosef Shiran
                                                  Title: Chief Executive Officer


Date: April 19, 2005
                                                  /s/ Gil Rozen
                                                  -------------
                                                  Name:  Gil Rozen
                                                  Title: Chief Financial Officer