The transmission of vibrations in the vicinity of a rectangular harmonic vertical load, acting on a viscoelastic layer overlaying a rigid half-space, is investigated theoretically, using a semi-analytic approach. The solution involves a double Fourier transform with respect to two of the space variables of Navier's elastodynamic equations. The inverse double Fourier transform is achieved with the FFT algorithm. Results presented include transformed displacements in the wavenumber domain, actual displacements in the near-field of the load, and the direct receptance at the load. (C) 1997 Academic Press Limited.