A continuum thermomechanochemical model of the behavior of a plastic-bonded explosive (PBX) 9501 formulation consisting of the energetic crystal octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) embedded in a polymeric binder is developed. Our main focus is on the study of the β↔δphase transformations (PTs) in crystalline HMX under a complex pressure-temperature path. To reproduce the pressure-temperature path, in particular during heating of PBX inside of a rigid cylinder, the β↔δ PTs in HMX are coupled to chemical decomposition of the HMX and binder leading to gas formation, gas leaking from the cylinder, elastic, thermal, and transformational straining as well as straining due to mass loss. A fully physically based thermodynamic and kinetic model of the β↔δ PT in HMX crystal is developed. It is based on a suggested nucleation mechanism via melt mediated nanocluster transformation and the recently revealed growth mechanism via internal stress-induced virtual melting. During the nucleation, nanosize clusters of the β phase dissolve in a molten binder and transform diffusionally into δ phase clusters. During the interface propagation, internal stresses induced by transformation strain cause the melting of the stressed δ phase much below (120 K) the melting temperature and its immediate resolidification into the unstressed δ phase. These mechanisms explain numerous puzzles of HMX polymorphism and result in overall transformation kinetics that is in good agreement with experiments. Simple phenomenological equations for kinetics of chemical decomposition of the HMX and the binder are in good correspondence with experiments as well. A continuum deformation model is developed in two steps. The geometrically linear (small strain) theory is used to prove that the internal stresses and macroscopic shear stresses are negligible. Then a large strain theory is developed under hydrostatic loading. The developed continuum thermomechanochemical model is applied in the accompanying paper [V. I. Levitas, B. F. Henson, L. B. Smilowitz, D. K. Zerkle, and B. W. Asay, J. Appl. Phys. (submitted)] to modeling the heating of PBX inside of a rigid cylinder.