In light of two wheel-rail contact relations, i.e., displacement compatibility and force equilibrium, a newly developed three-dimensional (3D) model for vehicle-track interactions is presented in this paper. This model is founded on the basis of an assumption: wheel-rail rigid contact. Unlike most of the dynamic models, where the interconnections between the vehicle and the track entirely depend on the wheel-rail contact forces, the subsystems of the vehicle and the tracks in the present study are effectively united as an entire system with interactive matrices of stiffness, damping and mass by the energy-variational principle and wheel-rail contact geometry. With wheel-rail nonlinear creepage/equivalent stiffness, this proposed model can derive dynamic results approaching to those of vehicle-track coupled dynamics. However, it is possible to apply a relatively large time integral step with numerical stability in computations. By simplifying into a linearized model, pseudo-excitation method (PEM) can be theoretically implemented to characterize the dominant vibration frequencies of vehicle-track systems due to random excitations. Finally, a trail method is designed to achieve the wheel climbing derailment process and a full derailment case where the bottom of the wheel flange has completely reached the rail top to form a complete derailment is presented.