The authors present a computational tool for simulating the wave propagation in arbitrary elastic medium. The goal is to provide a realistic simulation for seismic waves. The medium is assumed to be elastic and locally isotropic, but inhomogeneous. The authors employ the spectral element method, where the spatial discretization is performed by using quadrangles and hexahedra defined with respect to a reference unit domain by means of an invertible local mapping. The proposed approach has following features: a) inside each reference volume, the solution is expanded in discrete basis polynomials using Lagrange interpolants; by this way the mass matrix is always diagonal which allows a parallel implementation; b) the time discretization is based on an energy-momentum conservation scheme; c) instead of using quadrangles of infinite extent to model the infinite domain, the authors use finite extent domains with adequate impedance conditions (where the matching is more difficult due to the occurrence of longitudinal and transversal modes). Some numerical experiments are performed to validate the proposed method. First, an elastic medium bounded by a free surface is simulated, and long-term (about 140 s) energy and momentum conservations are found; then the authors obtain a rapid decay of energy for absobing boundaries. Some results for realistic cases are calculated and compared with those obtained by other numerical methods. The present method can be considered as a basic contribution to numerical methods in elastodynamics, but its application requires a large volume of computation. The authors give only the main ideas of the method and the obtained results; however, the paper provides the reader with a solid reference list (about 60 positions), related mostly to spectral element methods.