An analytical solution is developed for the problem of surface wave generation on a linear viscoelastic half-space by a finite rigid circular disk located on the surface and oscillating normal to it. The solution is an incremental advancement of theoretical work reported in articles focused on seismology. Since the application of interest here is medical diagnostics, the solution is verified experimentally using a viscoelastic phantom with material properties comparable to biological soft tissue. Findings suggest that prior estimates in the literature of the shear viscosity in human soft tissue may not be accurate in the low audible frequency range. Measurement of wave motion on the skin surface caused by internal biological functions or external stimuli has been studied by a few researchers for rapid, nonintrusive diagnosis of a variety of specific medical ailments. It is hoped that the developments reported here will advance these techniques and also provide insight into related diagnostic methods, such as sonoelastic imaging and other methodologies that utilize disease-related variations in tissue shear elasticity or variations in density due to gaseous inclusions.