▶ The effect of Ag content on the mechanical properties of Sn–Ag–Cu lead-free solders was studied systematically and the Ag content and strain rate-dependent material constitutive models have been developed for the first time. The effect of Ag content on the microstructures of Sn–Ag–Cu solder was also studied. The effect of Ni doping on the mechanical properties of Sn–1.0Ag–0.5Cu solder was also investigated and the temperature and strain rate-dependent material constitutive model has been developed for Sn–1.0Ag–0.5Cu–0.02Ni solder, which is essential for finite element simulation for assessment of reliability of electronic assembly with such solder. In this paper, the tensile tests were conducted at 25 °C to investigate the effect of Ag content and Ni doping on the microstructures and mechanical properties of Sn–3.0Ag–0.5Cu, Sn–2.0Ag–0.5Cu, Sn–1.0Ag–0.5Cu, Sn–1.0Ag–0.5Cu–0.05Ni and Sn–1.0Ag–0.5Cu–0.02Ni solders. The effect of strain rate on mechanical properties was investigated for each solder using stain rates of 10 −5 s −1, 10 −4 s −1, 10 −3 s −1, 10 −2 s −1 and 10 −1 s −1. In addition, the effect of temperature on mechanical properties was investigated for Sn–1.0Ag–0.5Cu–0.02Ni solder by conducting tests at −35 °C, 25 °C, 75 °C and 125 °C. Test results show that the elastic modulus, yield stress and ultimate tensile strength increase with increasing strain rate and Ag content, but they decrease with increasing temperature. The elastic modulus, yield stress and ultimate tensile strength are lower and the elongation is larger for Sn–1.0Ag–0.5Cu–0.05Ni solder compared with Sn–1.0Ag–0.5Cu–0.02Ni solder. The strain rate and Ag content dependent mechanical property models have been developed for Sn–Ag–Cu solders for the first time. In addition, the temperature and rate-dependent mechanical property models have also been developed for Sn–1.0Ag–0.5Cu–0.02Ni solder. The microstructures of solders were also analyzed. The Ag content affects Ag 3Sn intermetallic compound dispersion and Sn dendrite size. The microstructures of solder have fine Sn dendrites and more dispersed IMC particles for the high Ag content solder, which makes the solder exhibit high strength and yield stress.