As traditional lead-based solders are banned and replaced by lead-free solders, the drop impact reliability is becoming increasingly crucial because there is little understanding of mechanical behaviors of these lead-free solders at high strain rates. In this paper, mechanical properties of one lead-based solder, Sn37Pb, and two lead-free solders, Sn3.5Ag and Sn3.0Ag0.5Cu, were investigated at strain rates that ranged from 600 s−1 to 2200 s−1 by the split Hopkinson pressure and tensile bar technique. At high strain rates, tensile strengths of lead-free solders are about 1.5 times greater than that of the Sn37Pb solder, and also their ductility are significantly greater than that of the Sn37Pb. Based on the experimental data, strain rate dependent Johnson–Cook models for the three solders were derived and employed to predict behaviors of solder joints in a board level electronic package subjected to standard drop impact load. Results indicate that for the drop impact analysis of lead-free solder joints, the strain rate effect must be considered and rate-dependent material models of lead-free solders are indispensable.