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The numerical implementation of the direct boundary element method formulated for three-dimensional transient problems in elastodynamics is presented herein. In particular, a time-stepping algorithm for solving the convolution integrals appearing in the boundary integral formulation is discussed in detail, together with the fundamental solutions (Green's functions), which are the basic ingredient of the boundary element method. Next, advanced numerical integration techniques for evaluating kernel-shape function products over both singular and non-singular isoparametric surface elements and a scheme for computing stresses at the surface are described. The results obtained from application of this methodology to some selected test problems indicate the highly stable implicit nature of the formulation and that accurate results can be obtained over a wide range of time increments. (Author)