The subject of this paper is dust lifting behind shock waves, a process that is important for the formation of explosive dust clouds in air. While Eulerian-Eulerian has been the standard numerical technique for such simulations, the Eulerian-Lagrangian technique has been used in this paper, making it possible to take into account more physical phenomena, such as particle-particle and particle-wall collisions. The results of the simulations are shown mainly graphically, as snapshots of particle positions at given times after the passing of the shock wave. The results show that the collisions, and the coefficient of restitution assumed for them, is important in determining the mobility and lifting of dust behind shock waves. The results also show that the idea of a horizontally travelling shock wave is an oversimplification: the strong pressure gradient at the surface results in a series of reflected waves generated at the surface and travelling into the gas phase. (c) 2005 Elsevier Ltd. All rights reserved.