Predicting the fatigue life of solder interconnections is a challenge due to the complex nonlinear behavior of solder alloys and the load history. Long experience with Sn-Pb solder alloys together with empirical fatigue life models such as the Coffin-Manson rule have helped us identify reliable choices among package design alternatives. However, for the currently popular Pb-free choice of SnAgCu solder joints, designing accelerated thermal cycling tests and estimating the fatigue life are challenged by the significantly different creep behavior relative to Sn-Pb alloys. In this paper, a hybrid fatigue modeling approach inspired by nonlinear fracture mechanics is developed to predict the crack trajectory and fatigue life of a solder interconnection subjected to both isothermal accelerated thermal and anisothermal power cycling conditions. The model is shown to be similar to well accepted cohesive zone models in its approach and application and is anticipated to be computationally more efficient in a finite element setting. The approach goes beyond empirical modeling in accurately predicting crack trajectories. It is argued that such non-empirical models that capture the physics of material degradation and failure can form the basis for determining meaningful Pb-free solder environmental testing conditions as well as the acceleration factors relative to field use.