Abstract: To investigate high-speed train induced subground vibrations,viscoelastic half-space under moving loads was used to model thesubground under passing trains. Analytical solutions for displacements ofthe viscoelatic half-space were obtained using Green's function method forvarious moving loads, including constant and harmonic point, line and areaload. All velocity cases including the subsonic, transonic and supersonicvelocities were considered. Coupled IFFT algorithm and adaptive quadraturealgorithm were employed to compute double integrals in the analyticalsolutions. Numerical results for displacements induced by constant movingpoint load were presented in this paper as examples. The effects ofvelocity on the distribution and the maximum value of displacements were discussed. Itis found that the distribution and the maximum value of displacements varysignificantly as velocity increases beyond Rayleigh wave speed.