The numerical implementation of the direct boundary Element 4 formulation for time-domain transient elastodynamics analysis of tliree-dimensional cavities is presented. The present formulation employs the space and time dependent fundamental solution and dynamic reciprocal theorem to derive the boundary integral equations in the time domain. A time-stepping scheme is then used to solve the boundary initial value w problem by marching forward in time. Higher order shape function are used lo approximate the field quantities in space as well as in time, and a combination of analytical (time-integration) and numerical (spatial-inlegration) integration is carried out to form a system of linear equations. At the end of esch time step, these equations are solved to obtain the unknown field quantities at that time. Finally, the accuracy reliability of this algorithm is demonstrated by solving two examples for a spherical cavity under sudden radial expansion and spherical cavity under a pressure wave. Results are compared with the available analytical and numerical solution. The computer programs are written in Q.BASIC (Version 4.5) in addition CRAPHER (Version 1.75) is used to draw the results. The final version of the calculation are accomplished using the IBM 486 DX2-66MHz microcomputer at advanced computer lab., located at the Department of Mathematics and Computer Applications, College of Science, Saddam Uiuverstty.