The ignition behavior of polymer bonded explosives (PBXs) is critical to the safety assessments of weapons systems. The shock initiation experiment was designed to study this behavior. This article develops the constitutive model for the shock initiation of the PBX that includes viscoelastic response, statistical fracture mechanics, and an ignition hot spot mechanism. Friction heating on slip planes during plastic flow of explosives is considered as the main mechanism for the formation of hotspots and their ignition. Major results are the use of the ignition model for the PBX. The model was implemented in ABAQUS to predict the ignition of experiments. Computational results were verified by the experiments.