Railway vehicles can be viewed as complex multi-rigid-body systems composed of a body, frame, and wheelsets, with wheel-rail relationships exhibiting strong nonlinear characteristics. This chapter introduces the modeling methods for vehicle system dynamics under arbitrary geometric conditions. First, it briefly presents the multi-rigid-body dynamics methods suitable for vehicle modeling. Second, it discusses the geometrical relationships of wheel-rail contact and the theory of rolling contact between wheels and rails. Finally, it derives the motion equations of wheelsets and the complete vehicle motion equations under arbitrary geometric conditions in detail.