Compressive tests of Sn-4.5Zn-2Bi-In-P, Sn-9Zn-2.5Bi-In-P and Sn-8Zn-3Bi were conducted with gleeble1500 at constant temperature and strain rate. The conditions of the tests consisted of three temperatures 20, 60, 100 oC, and five strain rates 101, 100, 10-1, 10-2, 10-3. Results show that the saturation stress of three materials rises with the strain rate increasing, and decreases with the temperature increasing. In all experimental results, the saturation stress of Sn-8Zn-3Bi is maximum, and that of Sn-4.5Zn-2Bi-In-P is minimum. Nine parameters of Anand constitutive equation were confirmed for each kind of lead-free material by nonlinear fitting. By comparison and analysis between the experimental data and model prediction data of three materials under different conditions, the results show that Anand constitutive equation can describe the mechanical behaviors of three materials accurately, and supply a strong support for the reliability simulation and efficacy losing analysis.