Sn-Pb eutectic solder alloy is extensively used in microelectronics packaging interconnects. Due to the high homologous temperature, eutectic Sn-Pb solder exhibits creep-fatigue interaction and significant time-, temperature-, stress-, and rate-dependent material characteristics. The microstructure is often unstable, having significant effects on the flow behavior of solder joints at high homologous temperatures. Such complex behavior makes constitutive modeling an extremely difficult task. A viscoplasticity model unified with a thermodynamics-based damage concept is presented. The proposed model takes into account isotropic and kinematic hardening, and grain size coarsening evolution. The model is verified against various test data, and shows strong application potential for modeling thermal viscoplastic behavior and fatigue life of solder joints in microelectronics packaging.