The two-dimensional transient elastodynamic problems are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in spatial domain with the differential quadrature method (DQM) in time domain. The DRBEM with the fundamental solution of the Laplace equation transforms the domain integrals into the boundary integrals that contain the first- and the second-order time derivative terms. Thus, the application of DRBEM to elastodynamic problems results in a system of second-order ordinary differential equations in time. This system is then discretized by the polynomial-based DQM with respect to time. which gives a system of linear algebraic equations after the imposition of both the boundary and the initial conditions. Therefore. the solution is obtained at any required time level at one stroke without the use of an iterative scheme and Without the need of very small step size in time direction. The numerical results are visualized in terms of graphics. Copyright (C) 2008 John Wiley & Sons, Ltd.