The evaluation of running safety of railway vehicles on viaducts requires the study of lateral dynamics for the coupled vehicle-bridge system. This includes the structural deformation of the bridge, the vehicle multibody dynamics, and the consideration of wheel to rail contact. In this work, a fully nonlinear coupled method for such study is presented. The model is developed in a modular way using finite element models for the structure and multibody dynamics models for the vehicles in an absolute reference, and implemented within an existing finite element commercial code. A key feature is the consideration of the kinematics and dynamics of nonlinear wheel to rail interface, considering elastic-frictional contact. This contact is based on a global geometric constraint between wheelset and track and tangential forces at local level of each contact point. Some elementary applications are presented for the behavior of the model for stable and unstable hunting motion when subjected to transient lateral loads such as a wind gust. These results show the relevance of considering nonlinear effects and in particular wheel to flange contact.