A mathematical model of two-phase medium for the description of shock wave processes in gas particle suspensions with regard for particle-to-particle collisions is presented. The model is based on the molecular-kinetic approaches of theory of granular materials. A numerical technology for 2-D calculations is based on the Harten TVD scheme for gas and the Gentry-Martin-Daly scheme for particles. The effects of collisional particle dynamics are analyzed in shock-wave and detonation processes. In the flows of heterogeneous detonation in gas suspensions of reactive and inert particles the collisions of inert particles do not affect the detonation velocity, cell size, and cellular structures but provide spreading the inert phase layer-type structures in the far zone. The problems of a shock wave passage over a dense layer and of an explosive shock wave interaction with a layer are considered. It is confirmed a weak influence of the Saffman force and a significant effect of the Magnus force in the process of particle lifting from the layer directly behind the shock wave. It is shown that the development of chaotic motion and collisions is also one of the important mechanisms providing the dispersion of particles and formation of the dust clouds in the shock-wave processes. (C) 2015 Elsevier Ltd. All rights reserved.