A physical model is developed to describe the viscoelastic-plastic deformation, cracking damage, and ignition behavior of polymer-bonded explosives (PBXs) under mild impact. This model improves on the viscoelastic-statistical crack mechanical model (Visco-SCRAM) in several respects. (i) The proposed model introduces rate-dependent plasticity into the framework which is more suitable for explosives with relatively high binder content. (ii) Damage evolution is calculated by the generalized Griffith instability criterion with the dominant (most unstable) crack size rather than the averaged crack size over all crack orientations. (iii) The fast burning of cracks following ignition and the effects of gaseous products on crack opening are considered. The predicted uniaxial and triaxial stress-strain responses of PBX9501 sample under dynamic compression loading are presented to illustrate the main features of the materials. For an uncovered cylindrical PBX charge impacted by a flat-nosed rod, the simulated results show that a triangular-shaped dead zone is formed beneath the front of the rod. The cracks in the dead zone are stable due to friction-locked stress state, whereas the cracks near the front edges of dead zone become unstable and turn into hotspots due to high-shear effects.