In simulations of propagating blast waves the effects of artificial reflections at open boundaries can seriously degrade the accuracy of the computations. In this paper, a boundary condition based on a local approximation by a plane traveling wave is presented. The method yields small artificial reflections at open boundaries. The derivation and the theory behind these so-called plane-wave boundary conditions are presented. The method is conceptually simple and is easy to implement in two and three dimensions. These non-reflecting boundary conditions are employed in the three-dimensional computational fluid dynamics (CFD) solver FLACS, capable of simulating gas explosions and blast-wave propagation in complex geometries. Several examples involving propagating waves in one and two dimensions, shock tube and an example of a simulation of a propagating blast wave generated by an explosion in a compressor module are shown. The numerical simulations show that artificial reflections due to the boundary conditions employed are negligible. (C) 1998 John Wiley & Sons, Ltd.