''Visco-elastic drag'' associated with excitation of ground waves by a high speed train is investigated theoretically. Railway track is modeled by a beam that overlies a visco-elastic half-space. The train loading is described by a set of constant loads that uniformly move over the beam. The visco-elastic drag is calculated as the ratio of power (energy per unit time) of the track vibrations to the velocity of the train motion. Firstly, vibrations perturbed by a single load are considered to study dependence of the ''visco-elastic drag'' on the velocity of the load and on the material damping in the half-space. Secondly, by studying vibrations of the system under two loads, the effect of the distance between these loads to the visco-elastic drag is analyzed. Finally, total visco-elastic drag that is experienced by a TGV train is calculated and compared to the rolling drag and the aerodynamic drag.