Abstract In this paper, a two-phase mixture theory is presented which describes the deflagration-to-detonation transition (DDT) in reactive granular materials. The theory is based on the continuum theory of mixtures formulated to include the compressibility of all phases and the compaction behavior of the granular material. By requiring the model to satisfy an entropy inequality, specific expressions for the exchange of mass, momentum and energy are proposed which are consistent with known empirical models. The model is applied to describe the combustion processes associated with DDT in a pressed column of HMX. Numerical results, using the method-of-lines, are obtained for a representative column of length 10 cm packed to a 70% density with an average grain size of 100 μm. The results are found to predict the transition to detonation in run distances commensurate with experimental observations. Additional calculations have been carried out to demonstrate the effect of particle size and porosity and to study bed compaction by varying the compaction viscosity of the granular explosive.