In this article a numerical solution for a 3D isotropic, viscoelastic half-space subjected to vertical rectangular surface stress loading of constant amplitude is evaluated with the aid of the Radon and Fourier integral transforms. Dynamic displacement and stress fields are computed for the half-space surface as well as for points inside the domain. The analysis is performed in the frequency domain. Viscoelastic effects are incorporated by means of the elastic-viscoelastic correspondence principle. The equations of motion are solved in the Radon-Fourier transformed domain. Inverse transformations to the physical domain are accomplished numerically. The scheme used to perform the numerical inverse transformations is addressed. The solution is validated by comparison with results available in the literature. A sample of original dynamic results for displacement and stress fields for the 3D half-space is furnished. Copyright (c) 2006 John Wiley & Sons, Ltd.238787804