EXHIBIT 10 (B)(4)

                        TRANSAMERICA INCOME SHARES, INC.
                      FOR THE PERIOD ENDING MARCH 31, 2004
                            FORM N-CSR CERTIFICATION

    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 Certified Shareholder Report of Transamerica Income
Shares, Inc. (the "Fund") on Form N-CSR for the period ended March 31, 2004, as
filed with the Securities and Exchange Commission on the date hereof ("the
Report"), each of the undersigned hereby certifies that, to his knowledge:

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

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

      /s/ Brian C. Scott                                      Date: May 21, 2004
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      Brian C. Scott
      Director, President and Chief Executive Officer

      /s/ Kim D. Day                                          Date: May 21, 2004
      --------------
      Kim D. Day
      Senior Vice President, Treasurer and Principal Financial Officer

      /s/ John K. Carter                                      Date: May 21, 2004
      ---------------------------
      John K. Carter
      Senior Vice President, Secretary and General Counsel

A signed original of this written statement required by Section 906 of the
Sarbanes-Oxley Act of 2002 has been provided to the Registrant and will be
retained by the Registrant and furnished to the Securities and Exchange
Commission (the "Commission") or its staff upon request.

This certification is being furnished to the Commission solely pursuant to 18
U.S.C. Section 1350 and is not being filed as part of the Form N-CSR with the
Commission.