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, 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:September 9, 2004                  By:/s/ David M. Znamierowski
                                           ------------------------------
                                           David M. Znamierowski
                                           Its: President

Date:September 9, 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.