Wheelset dynamic analysis is a key element to determine the degree of accuracy of railway vehicle dynamics. In this study, a three-dimensional wheelset dynamic analysis is presented in such a way that the precise wheel-rail contact analysis in three-dimension is implemented into the dynamic equations of a wheelset. A numerical procedure that can be used for the analysis of a wheelset dynamics when the wheel-rail two point contact occurs in a cornering maneuver is developed. Numerical solutions of the constraint equations and the dynamics equations of a wheelset are achieved by using Runge-Kutta method. The proposed wheelset dynamic analysis is validated by comparison against results obtained from VI-RAIL analysis.