In the last forty years, researchers have developed models of wheel-rail contact force in order to study vibrations and rolling noise caused by railway traffic. These models range from analytical models, who consider a single rail of a railway track in contact with a rigid wheel attached to the bogie by means of the primary suspension, to numerical models based on finite element methods, boundary element, and mixed methods. Unlike analytical models, numerical models allow us to characterize more precisely the different components of railway track structure and consider the interaction between the entire track and a complete vehicle wheel-set. The study of the elements constituting the set of the railway track, the wheel-set and the primary suspension, as well as the knowledge of their influence in vibration generation and transmission due to train passage is of great interest when evaluating the possible vibration effects in the railway surrounding areas. This paper presents a numerical model of the track structure based on the finite element method. It is devoted to the study of the vibration response caused by vertical forces applied at any location on the rails. The numerical results are compared with analytical results previously presented in the bibliography.