A three-dimensional integral equation arises in the application of the boundary element method to transient dynamic problems of solid mechanics. The formulation has been given by Achenbach.(1) The time-domain boundary element formulation to solve this integral equation using constant elements has been implemented by Cole ct al.(2) To improve the accuracy of this method, higher-order shape functions in space and time have been used by Israil and Banajee(3) for two-dimensional problems. The numerical implementation of BEM far the time domain spherically symmetric transient problems has been given by Wang and Banerjee.(4) In this paper, a new and simpler fundamental solution for spherically symmetric transient elastodynamic problems is introduced. The BEM integral equation which is obtained using this kernel has no singularity on the boundary and is one-dimensional only. Using this formulation an example is solved of which analytical solution is given by Timoshenko and Goodier.(5) The same results have been obtained for the same problem by Wang and Banerjee. But they used a varying time interval to obtain identical results with analytical solution while here a constant time interval is used. Besides, our formulation provides the possibility of obtaining initial velocities for transient loadings applied to a medium at rest at t=0.