CERTIFICATION

            Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002


         Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections
(a) and (b) of section 1350, chapter 63 of title 18, United States Code), each
of the undersigned officers of The Hartford Income Shares Fund, Inc., does
hereby certify, to such officer's knowledge, that:

         The semi-annual report on Form N-CSR of The Hartford Income Shares
         Fund, Inc. for the period ending January 31, 2004 (the "Form N-CSR")
         fully complies with the requirements of Section 13(a) or 15(d) of the
         Securities Exchange Act of 1934 and information contained in the Form
         N-CSR fairly presents, in all material respects, the financial
         condition and results of operations of the Fund.

Date:  March 10, 2004               By: /s/ David M. Znamierowski
                                        ----------------------------------------
                                        David M. Znamierowski
                                        Its: President

Date:  March 10, 2004               By: /s/ Tamara L. Fagely
                                        ----------------------------------------
                                         Tamara L. Fagely
                                         Its: Vice President, Controller and
                                         Treasurer

A signed original of this written statement required by Section 906 has been
provided to The Hartford Income Shares Fund, Inc. and will be retained by The
Hartford Income Shares Fund, Inc. and furnished to the Securities and Exchange
Commission or its staff upon request.