The interesting and common situation of shallow point sources close to the free surface can be modeled using an explicit elastic finite difference procedure. If the source depth is less than the predominant wavelength from the surface or other well-defined elastic boundary, then shear waves S*, are generated with an amplitude which depends strongly on the source depth. As the source depth is decreased, the amplitude of the resulting shear wave increases exponentially and the particle motion is confined to a plane perpendicular to the direction of propagation. These shear waves radiate from a point on the boundary directly above the source with a radiation pattern that is zero at grazing incidence, rises to a positive maximum at about 55° from the vertical, changes polarity, and increases negatively until merging with the PS wave. Since the use of shallow explosive sources for seismic exploration is favorable for the generation of S*, we present a field data case as an illustration.