The running safety of railway vehicles on structures subjected to earthquake motion has been studied using a computer simulation program “DIASTARS” to analyze the dynamic interaction problem between vehicle and structure. In the simulation program, not only the nonlinearity of primary and secondary suspensions of vehicle but also the hysteretic characteristics of structure are taken into consideration. Through the analysis, several running safety boundary diagrams with respect to the frequency of applied sinusoidal motion and the natural period of structure are obtained. The influence of nonlinear behavior of structure on the running safety boundary diagram is also discussed.