The derailment model of a 51-DOF railway vehicle including coupling effects of the longitudinal and lateral modes was theoretically built by investigating the geometrical and dynamical effects of the lateral acceleration, gyro factors and mechanical factors such as flange angle, friction coefficient, effective radius of the wheel and track gauge. The lateral dynamic of the railway vehicle comprising lateral, vertical displacement and roll, yaw, pitch angular displacements of each six wheelset, three bogie frames, and vehicle body was modeled in detail. Depending on this model, the initiation of different kind of derailments such as wheel lifting, wheel climbing, roll-over and their synthesis can be predicted. In addition, the effects of vehicle speed on derailment quotient (DQ)'s were investigated under various suspension parameters and curved track radius. Main objective of the development of such a numerical model is to analyze various dynamical and geometrical influences on the wheelset, which is not considered in conventional derailments models such as those based on Nadal and Weinstock criteria.