It is known that the tensile strain tolerance of the critical current of Bi2223 composite superconductors is improved when the compressive residual strain of Bi2223 filaments in the current transport direction (sample length direction) is enhanced. In the present work, the thermally and mechanically induced residual strain accumulation process of a stainless steel-laminated Bi2223/Ag/Ag alloy superconducting composite tape fabricated at American Superconductor Corporation was studied. A calculation procedure is presented for a description of the strain change of the constituents (Bi2223, Ag, Ag alloy and stainless steel) during cooling and heating, and during lamination, followed by the stress relaxation. As the input values, the mechanical property values of the constituents and the residual strain of Bi2223 filaments in the laminated composite tape at room temperature, measured with x-rays, were used. Such an approach revealed the change of residual strain of each constituent in the thermal and mechanical process in the laminated composite tape. Then, from a comparison of the residual strain accumulation in the laminated tape with that in the insert tape, the effects of the stainless steel lamination on the enhancement of the compressive residual strain of Bi2223 filaments and the improvement of the tensile strain tolerance and strain tolerance window of critical current at 77 K of the composite tape are discussed.