The exact analytical solution for surface displacements due to a volumetric linesource disturbance buried in an elastic homogeneous and isotropic half-space is arguably due to W. W. Garvin. In this work we present a generalization in the three-dimensional space of the algorithm of Garvin’s problem presented by Sanchez-Sesma and Viveros in 2006 for a point source of compressional elastic waves. Our solution can be used as a practical tool to test 3D numerical techniques devoted to simulation of the interaction dynamics between seismic radiation and near-surface geological structures. Such numerical techniques have shown to be well suited for assessing strong ground motion features. These latter represent one of the first useful information aimed at assessing the damage scenarios due to an earthquake in urban areas. Some examples are presented, and synthetic seismograms and polarigrams are displayed.