Localized heating of granular energetic solids due to low speed piston impact (~100 m/s) can initiate chemical reaction and ultimately lead to Deflagration-to-Detonation Transition (DDT). Largely motivated by safety concerns, mathematical modeling has been used to gain insight into the physical processes involved. Most models are based on principles of continuum mixture theory as it is presently impractical to track (and numerically resolve) the complex dynamics of a large number of small grains (~ 1014 grains/m3) over typical lengths associated with DDT (~ 5 cm). This talk will address issues concerning the continuum modeling of compaction induced localized heating of granular HMX. Only the thermo-mechanical response of the granular solid is considered; thus, the solid is assumed to be inert and gas phase effects are ignored. The model, which is an extension of the single phase limit of two-phase DDT models, better accounts for the energetics and dissipation of the compaction process than do conventional models. The model predicts results commensurate with experiments for both quasi-static and dynamic compaction of granular HMX including stress relaxation, hysteresis, and substantial dissipation. A steady, 1-D compaction wave analysis in which bulk dissipated energy is locally deposited within the compaction zone structure over the surface of grains, and the evolution of the temperature field within grains is tracked, shows the formation of thin regions of localized heating near the grain surface. Based on predicted "hot-spot" temperatures, a two-phase thermal explosion analysis gives estimates for the explosion threshold as a function of grain size and piston impact speed which compare favorably with experimental DDT data for granular HMX. Also, 1-D piston supported compaction of granular HMX having spatially non-uniform initial porosity is explored by numerically integrating the unsteady model using a high-resolution ENO method and parallel processing techniques.