Abstract This paper presents a theoretical study of the steady state dynamic response of a railway track to a moving train. The model for the railway track consists of two beams on periodically positioned supports that are mounted on a visco-elastic 3D layer. The beams, supports, and layer are employed to model the rails, sleepers and soil, respectively. The axle loading of the train is modeled by point loads that move on the beams. A method is presented that allows to obtain an expression for the steady-state deflection of the rails in a closed form. On the basis of this expression, the vertical deflection of the rails and its dependence on the velocity of the train is analyzed. Critical velocities of the train are determined and the effect of the material damping in the sub-soil and in the pads on the track response at these critical velocities is studied. The effect of the periodic inhomogeneity of the track introduced by the sleepers is studied by comparing the dynamic response of the model at hand to that of a homogenized model, in which the supports are assumed to be not discrete but uniformly distributed along the track. It is shown that the vertical deflection of the rails predicted by these models resemble almost perfectly. The elastic drag experienced by a high-speed train due to excitation of track vibrations is studied. Considering a French TGV as an example, this drag is calculated using both the inhomogeneous and homogenized models of the track and then compared to the rolling and aerodynamic drag.