The direct 3D method of numerical simulation of gasless combustion of mechanically activated solid powder mixtures is developed. The method under consideration falls into three stages. On the first stage, a simulation of mixture structure is performed. An analysis of the structure obtained in simulations is carried out. On the second stage, the thermal conductivity of solid powder mixture is calculated. On the third stage of simulation, the ignition and combustion of each particle of the mixture is considered with taking into account of heat exchange between contacting particles. The results of numerical simulations are represented dynamically and compared with the experimental data, obtained by high-speed digital recording of mechanically activated SHS systems combustion.