The track ground dynamic response induced by the passage of high speed trains is studied based on a three-dimensional finite element (FE) coupled train-track model. Particular emphasis is placed on the investigation of the effect of the train fundamental passing frequency on the level of ground vibration, when it exceeds the ground cutoff frequency, as the train speed increases or the clay depth changes. The developed model uses twenty node brick elements to represent the track components such as the sleepers, the ballast and the subgrade. The rail is described by the three-dimensional Euler-Bernoulli beam element. A quarter train model, including primary and secondary suspensions, is coupled to the three-dimensional railway track model by virtue of the nonlinear Hertzian contact theory. The proposed three-dimensional finite element (FE) model incorporates multi-layered ground and radiation damping, by using viscous boundary conditions. Material non-linearity, especially of the ballast layer could be taken into account. Preliminary numerical experiments show that high levels of vibrations can be produced for supercritical train speeds leading to a train passing frequency exceeding the ground cutoff frequency.