Deflagrations of solid reactants have been widely studied in the context of self-propagating high-temperature synthesis. Propagating velocities of the order of sound speed or faster have not been contemplated due to the belief that the processes determining thermal conduction and diffusion cannot support those rates. Experiments, by Enikolopyan, Gogulya and others, however; disproved those notions. A model for solid-solid reactions, which describe deflagration and detonation, is presented. The fluctuation energy is large and the system requires significant preheating before ignition occurs. Based on experimental observations, the activation energy of a compressed system is lowered by the amount of elastic work done during compression. This phenomenon is included in the model. Ignition by impact and external thermal sources are investigated and detonations develop only in the case of impact initiation. Interactions between the shock front and the reaction front are also investigated.