Solder joint fatigue failures are a potential reliability hazard in surface-mount electronic packages under cyclic thermal loading environment.  Proper design and reliability assessment requires accurate modeling of the stress and strain fields within the solder joint.  Some of the existing closed-form stress analysis models tend to oversimplify the complicated elastic, plastic and viscoplastic stress state in the solder joint, and thus fail to give 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 refined in this paper to obtain the stress field in J-leaded surface-mount solder joints, under cyclic thermal loading.  The method can also be applied to other surface-mount lead and solder joint configurations such as gull-wing, leadless, ball-grid and column-grid joints.  The solder domain is selectively discretized into colonies of nested sub-domains only where large thermal expansions mismatch.  The number of colonies and the number of sub-domains within each colony can be varied for optimum accuracy.  The Rayleigh-Ritz energy method based on a multi-field displacement assumption is used to estimate the deformation, strain and stress fields within the solder domain.  In the present paper, the potential energy stored in the and in the Printed Wiring Board (PWB) segment, both of which are total potential energy enables modeling of the deformation caused by both the global and local CTE mismatches.  This work represents a significant improvement over a previous paper presented by the authors, where the global CTE mismatch was by Rayleigh-Ritz energy scheme and the local CTE mismatch was estimated by an existing one-dimensional eigen-function analysis fir interfacial stresses at interfaces of dissimilar materials [Dasgrupta et. al., 1993].  Moreover, the previous paper could use only one sub-domain for displacement enhancement.  The present model therefore has more generalized capabilities than the work reported before.  Results of two-dimensional elastic analysis are presented in this paper.  Plastic and creep deformation can be modeled with this scheme by using incremental load-stepping and/or time-stepping techniques, and will be presented in a future paper.  The final goal is to predict the stress, strain and strain energy density distributions in the solder domain with good accuracy, but at a fraction if the computational effort typically required in a full-scale finite element analysis.  The fatigue endurance of the solder joints can be assessed by combining results from this stress analysis model with an appropriate damage model.