Significant reductions in the solder-joint interconnect size results in the increased volume fraction of brittle intermetallics in the joint. Previously, the prevalent failure mode in a solder joint was the ductile thermo-mechanical fracture of solder material due to repeated thermal cycling. In addition to this mode of failure the joints were also found to fail by brittle fracture near the solder-intermetallic interface. To predict and reduce the failure of a solder joint, a model that incorporates both plastic damage in bulk solder and solder-intermetallic interface failure is timely and useful to the electronics industry. Based on cohesive fracture theory, a 3D finite element model has been developed to predict the interfacial damage of different solder interconnects. Unified creep-plasticity theory is incorporated in the model considering the creep and hysteresis effects in solder bulk. Using the unified creep-plasticity-cohesive finite element model, the intermetallic-layer growth effect has been researched for different solders.