In this paper, a method is proposed for the modeling of dynamic wheel/rail frictional rolling contact. A full finite element formulation around the stationary position in an Eulerian reference frame is derived with a fine discretization of the contact surface combined with unilateral and Coulomb friction laws. Appropriate numerical techniques and reduction strategies are used in order to solve the non linear discrete equations in dynamic self-sustained conditions. In addition to the transient approach, a stability analysis allows the determination of unstable modes. This methodology is currently used in realistic wheel/rail contact in curves to simulate curve squeal.