The understanding of the strain dependence of critical current, $I_c$, in the reversible region is important for the evaluation of the performance of coated conductor (CC) tapes in practical applications. In this study, the stress/strain tolerance of $I_c$ in GdBCO CC tapes with stainless steel substrate stabilized by additional Cu and brass laminate was analyzed quantitatively through $I_c$-strain measurement at 77 K under self-field. The variation in irreversible strain limits of CC tapes by the addition of stabilizing layers was analyzed through the consideration of the pre-strain induced on the GdBCO coating film. The results were then compared with the ones previously reported for GdBCO CC tapes with Hastelloy substrate. As a result, GdBCO CC tapes with stainless steel substrate showed much higher strain tolerance of $I_c$ as compared with those adopting Hastelloy substrate.