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 ended January 31, 2006 (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 9, 2006                   By: /s/ David M. Znamierowski
                                           -------------------------
                                           David M. Znamierowski
                                           Its: President


Date:  March 9, 2006                   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.