Accurate prediction of vehicle curve negotiation performance is critically important for evaluation of railway vehicle safety. Although multibody dynamics vehicle simulation has been widely utilized for the vehicle performance evaluation, nonlinearities associated with the air suspension behavior are vastly simplified and the air mass flows of the leveling valve (LV) and differential pressure valve (DPV) are neglected in many cases. It is, however, known that changes in the air spring pressure caused by the LV and DPV make a non-negligible impact on the vertical wheel load variation and the derailment safety in small radius curved tracks. Therefore, this paper presents a numerical procedure for the analysis of the coupled vehicle and air suspension system behavior, considering nonlinearities associated with LV and DPV flow characteristics. To enable quick and accurate prediction of the history-dependent LV-induced wheel load unbalance and its impact on the derailment safety, quasi-static vehicle motion solvers for the fully coupled vehicle and air spring system flow equations are developed. Several numerical examples are presented to demonstrate the simulation capabilities developed in this study and numerical results are validated against the test data.