This paper presents a comprehensive approach for the mathematical and computer modeling of subsystems required in vehicle dynamic simulations. Three dimensional models for tire-terrain interaction, traction, braking, steering, and suspension systems are presented. The tire-terrain interaction model provides the necessary tire forces and moments which are determined by explicit formulation or experimental data based model. For the suspension subsystem, such elements as bushing, leaf spring, and stabilizer bar are reviewed. For the steering, traction, and braking subsystems, simplified models are discussed. The models developed here can easily be implemented in a three dimensional multibody simulation program.