A tensile test was conducted to evaluate thermal fatigue resistances of Sn-Bi (-Ag) and Sn-Ag-Bi-Cu lead-free solder alloys. The test is based on the strain rate change method to obtain a strain rate sensitivity index (SRSI), m. The m values were investigated at various strains during the tensile test, until fracture. The plots of m and strain where m is measured showed a linear relationship. Therefore, the m value at zero strain, m0, and the gradient of the fitting line, k, were obtained by extrapolation. Using m0 and k values, an estimation of the thermal fatigue resistance of the solder joint was attempted. It was believed that m0 and k can be taken as a guide for developing a new lead-free solder with the excellent thermal fatigue resistance. Moreover, the influences of the aging treatment on m0, k and the microstructure of the solder were also investigated.