Critical hunting speed and running safety are important aspects of the dynamic behaviour of railway vehicles. In this seminar, a study of the dynamic behaviour of a single railway vehicle truck running on tangent and curved tracks is carried out using a mathematical model of the combined system. It is seen from literature that there are no reported studies using the combined truck/track system in which rail lateral displacement is computed considering two point wheel/rail contact for evaluation of critical hunting speed, as well as derailment due to wheel climb. The truck consists of the truck frame with suspended wheel-axle sets, while the track is idealized as a laterally flexible rail modelled as a spring-mass-damper system. The combined truck/track system has 10 degrees of freedom (DOF), consisting of the lateral displacement and yaw angle of the wheel-axle sets and truck frame, as well as the l ateral displacement of the front and the rear left and right rails. Equations of motion using single-point and two-point wheel-rail contact are derived. The longitudinal and lateral primary and secondary suspensions are assumed to have linear stiffness and damping characteristics. A combination of linear Kalker’s theory and non-linear heuristic creep model is adopted to calculate the creep forces. The mathematical equations of motion are solved using fourth order Runge-Kutta method. The transformed state space equations are solved in the time domain to obtain the dynamic response of a conventional truck, moving on tracks of various radii. Finally, the effect of primary suspension, wheel conicity, superelevation angle and radius of curvature of the track, on the running safety, is assessed. The numerical simulation is done using MATLAB.