In this study, a space-time discontinuous Galerkin formulation is derived for dynamic analysis of solids. Numerical implementation of proposed formulation is presented, and numerical examples are provided for shock wave propagation problems. Numerical results are compared with that of the known exact solutions of the problems and numerical results obtained from a commercial finite element code. The proposed space-time discontinuous Galerkin formulation is found to be robust and Successful in modelling transient problems, i.e. shock wave propagation problems. Copyright (C) 2007 John Wiley & Sons, Ltd.