Microelectronic systems are subjected to thermal cycling, power cycling, and vibration environments in various applications. These environments, whether applied sequentially or simultaneously, affect the solder joint reliability. Literature is scarce on predicting solder joint fatigue failure under such multiple loading environments. This thesis aims to develop a unified modeling methodology to study the reliability of electronic packages subjected to thermal cycling, power cycling, and vibration loading conditions. Such a modeling methodology is comprised of an enriched material model to accommodate time-, temperature-, and direction-dependent behavior of various materials in the assembly, and at the same time, will have a geometry model that can accommodate thermal- and power-cycling induced low-cycle fatigue damage mechanism as well as vibration-induced high-cycle fatigue damage mechanism. The developed modeling methodology is applied to study the reliability characteristics of ceramic area array electronic packages with lead-based solder interconnections. In particular, this thesis aims to study the reliability of such solder interconnections under thermal, power, and vibration conditions individually, and validate the model against these conditions using appropriate experimental data either from in-house experiments or existing literature. Once validated, this thesis also aims to perform a design of simulations study to understand the effect of various materials, geometry, and thermal parameters on solder joint reliability of ceramic ball grid array and ceramic column grid array packages, and use such a study to develop universal polynomial predictive equations for solder joint reliability. The thesis also aims to employ the unified modeling methodology to develop new understanding of the acceleration factor relationship between power cycling and thermal cycling. Finally, this thesis plans to use the unified modeling methodology to study solder joint reliability under the sequential application of thermal cycling and vibration loading conditions, and to validate the modeling results with first-of-its-kind experimental data. A nonlinear cumulative damage law is developed to account for the nonlinearity and effect of sequence loading under thermal cycling, power cycling, and vibration loading.