Summary: The interaction between railway vehicle and bridge is dynamic and nonlinear in nature. This paper aims to develop a computer-aided numerical method for analyzing coupled railway vehicle-bridge systems of nonlinear features. The finite element method is used to establish not only a bridge model (bridge subsystem) but also flexible vehicle models (vehicle subsystem). The connections between the two subsystems are considered through wheel-rail contact models with and without wheel jumps. All the nonlinear forces and concentrated damping forces in the two subsystems and the nonlinear contact forces at their interface are treated as pseudo-forces to facilitate nonlinear analysis. The mode superposition method is then applied to the two subsystems, and both non-iterative and iterative computation schemes are utilized to find the best solution. The convergence of iterative computation schemes is investigated with and without wheel jumps. The explicit integration scheme is found to possess higher convergence than other schemes. The applicability and accuracy of the proposed numerical method are finally illustrated through numerical examples and comparisons with previous work.