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 annual report on Form N-CSR of The Hartford Income Shares Fund,
         Inc. for the period ended July 31, 2005 (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: September 9, 2005                 By: /s/David M. Znamierowski
                                            -------------------------
                                            David M. Znamierowski
                                            Its: President


Date: September 9, 2005                 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.