In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and their effect on the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions [Towashiraporn, , 2005, “A Hybrid Model for Computationally Efficient Fatigue Fracture Simulations at Microelectronic Assembly Interfaces,” Int. J. Solids Struct., 42(15), pp. 4468–4483]. We review well understood principles in elastic-plastic fracture mechanics and more recent work in cohesive zone modeling, that address the nature of the singular solutions at the crack tip and provide insight when dealing with the more complex problem of solder joint fracture. Using three-dimensional finite element analysis of a chip scale package, we systematically examine the stress-strain behavior at the edge of the solder joint along the interface. The singular nature of the behavior manifests itself as mesh dependence of the predicted crack front shape and the cycles to failure. We discuss the conditions under which the predicted crack growth rate is of reasonable accuracy by incorporating a characteristic length measure. We validate predictions made by the hybrid damage modeling approach against a companion experimental study in which crack growth was tracked in packages subjected to accelerated thermal cycling.