The processes of coal dust-air mixtures motion, ignition, and combustion behind shock waves have been numerically studied using physically justified types of flow description. In the paper, several aspects of unsteady processes behind shock waves propagating in long ducts (tunnels) with thin layers of dust and filled with air are studied. Numerical methods have been developed to solve the considered problems. Some examples of calculations have been presented: dust entrainment and dispersion from dense layers behind propagating shock waves, as well as dispersion, ignition and combustion of dusty mixtures due to a local gas explosion in a long tube.