The problem of solder joint fatigue is essentially one of fatigue crack growth. However, little work has been done that enables fatigue life predictions by means of tracking the crack front and its growth. Most popular fatigue life models are empirical and therefore, limited in their applicability and in the insight they provide. Analytical fracture mechanics approaches such as the Paris Law and the J-Integral are of questionable validity due to the fact that several assumptions made in these approaches are not appropriate in the context of solder joint fatigue. Failure in solder joints involves large plastic deformation in a viscoplastic material along with crack growth which is not self-similar and is significantly large relative to the size of the joint. Accurate descriptions of crack growth in solder joints can thus be obtained only by means of an approach that includes (a) the complete constitutive behavior of solder and (b) a non-empirical failure model that does not make the limiting assumptions of small cracks or self-similar crack growth. One such promising approach is the hybrid damage modeling approach, which is inspired by cohesive zone modeling and Weibull functions . In this study, we focus on investigating the nature of the stress and strain behavior in solder joints and its effect on the hybrid model. 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 (CSP), we systematically examined 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 incorporation of 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. In the first part, presented here, we study the effects of choice of constitutive model (elasticity, deformation and incremental plasticity and creep) and finite deformation on the nature of the singularity at the crack tip and the resulting mesh sensitivity. We use a conventional crack-in-plate analysis to first study the effects and then investigate similar effects in the more complex problem of a solder joint. In the second part, a characteristic length is introduced in an attempt to mitigate the mesh dependence, and shown to improve results for the predictions of crack growth in both, the crack-in-plate and the solder joint models.