Solder joint fatigue failures are a potential reliability hazard in surface-mount electronic packages under cyclic thermal loading environment. Proper design and reliability assessment are thus crucial to ensure the fatigue endurance of the electronic packages. Accurate modeling of the stress and strain fields within the solder joint under cyclic thermal loading condition is of extreme importance since ultimately, a reasonable fatigue life estimation depends not only on a appropriate fatigue model, but more fundamentally, on accurately predicted stress and strain fields. Modeling stress and strain fields in solder joint in surface-mount electronic packages have never been an easy task since solder undergoes elastic, plastic and time dependent creep during each loading and unloading cycle. Some of the existing closed-form stress analysis models tend to oversimplify this complicated viscoplastic stress state, thus failing to give a reasonable prediction of the solder joint fatigue endurance. Extensive finite element analyses require prohibitive investment in terms of the analysis time and analyst expertise, especially when full scale elastic, plastic and creep analyses are performed. A generalized multi-domain approach proposed earlier by the authors is further developed in this paper to obtain the stress and strain fields in J-leaded surface-mount solder joint undergoing elastic-plastic deformation, under cyclic thermal environment (Ling et al., 1995). The Rayleigh-Ritz energy method based on a multi-field displacement assumption is used. In a previous paper (Ling et al., 1995), the results for analysis within elastic region had been demonstrated and were proved to be in agreement with finite element analysis. In this paper we further develop the methodology into plastic deformation region. Hysteresis loops for both the global and the local CTE mismatch problem can finally be generated. Results for two-dimensional elastic-plastic analysis are presented in the current paper. Creep deformation can be further modeled with this scheme by using time-stepping incremental techniques, and will be presented in a future paper. The final goal of this research is to predict the stress, strain and energy density distributions in the solder joint with reasonable accuracy. The fatigue assessment of the solder joint can then be performed by combining results from this stress analysis model with an appropriate damage model, for example, the energy-partitioning fatigue model (Dasgupta et al., 1992).