The significant difference between failure modes of lead-containing and lead-free solder joints under drop impact loading remains to be not well understood. In this paper, we propose a feasible finite element approach to model the cracking behavior of solder joints under drop impact loading. In the approach, the intermetallic compound layer/solder bulk interface is modeled by the cohesive zone model, and the crack driving force in the intermetallic compound layer is evaluated by computing the energy release rate. The numerical simulation of a board level package under drop impact loading shows that, for the lead-containing Sn37Pb solder joint, the damage in the vicinity of the intermetallic compound layer initiates earlier and is much greater than that in the lead-free Sn3.5Ag solder joint. This damage relieves the stress in the intermetallic compound layer and reduces the crack driving force in it and consequently alleviates the risk of the intermetallic compound layer fracturing.