The main goal of this paper is to shed light on the effect of strain rate and viscoplastic deformation of bulk solder on the interfacial failure of lead-free solder joints. For this purpose, interfacial damage evolution and mode I fracture behavior of the joint were evaluated experimentally by performing stable fracture tests at different strain rates employing an optimized tapered double cantilever beam (TDCB) design. The viscoplastic behavior of the solder was characterized in shear, and the constitutive parameters related to the Anand model were determined. A rate-independent cohesive zone damage model was identified to best simulate the interfacial damage progression in the TDCB tests by developing a three-dimensional (3D) finite-element (FE) model and considering the viscoplastic response of the bulk solder. The influence of strain rate on the load capability and failure mode of the joint was clarified by analyzing the experimental and simulation results. It was shown how, at the lower strain rates, the normal stress generated at the interface is limited by the significant creep relaxation developed in the bulk solder and thus is not sufficiently high to initiate interfacial damage, whereas at higher rates, a large amount of the external energy is dissipated into interfacial damage development.