Abstract: To investigate vibrations of subground induced by high-speed trains,the viscoelastic half-space subjected to moving loads was used to model the subground under running trains.Analytical solutions for dynamic responses,including displacement,velocity and acceleration,were developed by Fourier integral transform.Coupled IFFT algorithm and adaptive quadrature algorithm was employed to compute double integrals in the analytical solutions.All the subsonic,transonic and supersonic cases were computed.The effects of velocity on the maximum responses and their distribution were discussed.It was found that the maximum and distribution of dynamic responses varied significantly as velocity increased beyond Rayleigh wave speed.