The thermal integrity of an electronic package depends on the strength of the interface between dissimilar materials. Due to high thermo-mechanical stress concentrations arising from large temperature excursions, electronic packages become prone to cracking at regions with geometric and/or material discontinuities. Thus, the accurate calculation of the thermo-mechanical stresses in regions of high stress concentrations is critical to achieving a reliable design. These high-stress-concentration regions pose a major concern, especially in the design of flip-chip packages. Understanding the mechanisms for relaxing the high stress concentrations through the use of appropriate material properties, bump and adhesive joint geometry, and filler size in a flip-chip package will aid in design improvements for ensuring the thermomechanical reliability of electronic packages. In this study, the effect of underfill on the level of stress concentrations is investigated and possible failure sites are identified by using a global/local finite element approach. The global elements capture the exact singular behavior of the stresses near the geometric and material discontinuities. Potential failure sites are established by applying concepts from fracture mechanics.