A series of multiaxial ratcheting tests were conducted on 63Sn–37Pb solder. A unified viscoplastic constitutive model was developed on the basis of the Ohno–Wang kinematic hardening model, and the rate dependence of the material was taken into consideration by introducing a viscous term. The stress-strain hysteresis loop of 63Sn–37Pb under different strain rates can be simulated reasonably well by the model. However, since the axial ratcheting strain rate of 63Sn–37Pb solder is strongly dependent on the applied shear strain rates in axial/torsional ratcheting, the original constitutive model fails to describe the effect of shear strain rate on the ratcheting strain. To improve the rate sensitivity of the model, the material parameter was correlated to the strain rate. Comparisons of the experimental and simulated results verify that the modified constitutive model is able to predict the complicated deformation of 63Sn–37Pb. The effects of axial stress, shear strain range, loading history, and strain rate on ratcheting behavior can be reflected fairly well.