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Electromigration (EM) and thermomigration (TM) are processes of mass transport which are critical reliability issue for next generation nanoelectronics. The purpose of this project is to study the influence of low temperature on EM and TM interaction. In this paper, a model for EM and TM process is proposed and has been implemented in finite element method. The governing equations include mass conservation, force equilibrium, heat transfer, and electricity conduction equations. A damage evolution model based on thermodynamics is introduced to evaluate the degradation in solder joints subjected to high current densities and high temperature gradients. The results are compared with experimental data to validate the model.