Large Eddy simulation (LES) of shock/homogeneous turbulence have been performed at two different Mach numbers (1.2 and 2) with four different subgrid scale (SGS) models (Smagorinsky model, mixed scale model, dynamic Smagorinsky model, dynamic mixed model). The code was successfully validated by comparisons with the direct numerical solutions (DNS) results of Lee et al. and, from a numerical point of view, the hybrid flux approach presented here exhibits a very satisfactory behaviour. The general conclusion of this study is that LES is efficient for such an interaction only if the mesh is fine enough in the shock vicinity to capture shock corrugation. Even with such a requirement, LES reduces dramatically the computational effort necessary to simulate the shock/homogeneous turbulence interaction with respect to DNS. Dynamic SGS models are found to improve markedly the quality of the results when compared to simple models like Smagorinsky's. (C) 2001 Elsevier Science Ltd. All rights reserved.