The aim of this paper is to develop a full Finite Element (FE) computational method for the dynamics of wheel/rail frictional rolling contact systems in order to calculate reference solutions in curve squeal. The proposed method is characterized by the use of a fine FE discretization of the contact surface in an Eulerian frame, non-smooth frictional contact laws and model reduction techniques. An application to the wheel/rail frictional rolling contact is presented in both quasi-static and dynamic cases. The validation of the approach in quasi-static conditions is carried out by comparison with CONTACT software. Stability and transient results show that the technique is able to simulate friction-induced vibrations at high frequencies.