A new method for wheel-rail multi-point contact is presented in this paper. In this method, the first- and the second-order derivatives of the wheel-rail interpolation distance function and the elastic wheel-rail virtual penetration are used to determine multiple contact points. The method takes account of the yaw angle of the wheelset and allows the identification of all possible points of contact between wheel and rail surfaces with an arbitrary geometry. Static contact geometry calculations are first carried out using the developed method for both new and worn wheel profiles and with a new rail profile. The validity of the method is then verified by simulations of a coupled vehicle and track system dynamics over a small radius curve. The simulation results show that the developed method for multi-point contact is efficient and reliable enough to be implemented online for simulations of vehicle-track system dynamics.