Taylor blast wave (TBW) theory and geometrical shock dynamics (GSD) theory describe a radially expanding shock wave front through an inert material, typically an ideal gas, in the strong blast wave limit and weak acoustic limit respectively. We simulate a radially expanding blast shock in air using a hydrodynamic simulation code and numerically describe the intermediate region between these two limits. We test our description of the intermediate shock phase through a two-dimensional simulation of the Bryson and Gross experiment. We then apply the principles of GSD to materials that follow the Mie–Gruneisen equation of state, such as plastics and metals, and derive an equation that accurately relates the acceleration, velocity and curvature of the shock through these materials. Along with detonation shock dynamics (DSD), which describes detonation shock propagation through high explosive fluids, we develop a hybrid DSD/GSD model for the simulation of heterogeneous explosives. This model enables computationally efficient simulation of the shock front in high explosive/inert mixtures consisting of simple or complex geometric configurations. We simulate an infinite two-dimensional slab consisting of one half explosive, PBXN-9, and one half aluminium and model the boundary angle conditions using shock polar analysis. We also simulate a series of high explosive unit cells embedded with aluminium spherical particles, and we compare the propagation of the detonation shock front with a direct numerical simulation performed with the ALE3D code.