This paper proposes a novel modeling methodology of vehicle dynamics to reproduce the actual three-dimensional rotating motion. In the proposed approach, a rigid body of vehicle is physically modeled with constraint force, where Euler's equation of motion is applied to numerically calculate rotating behaviors around the center of gravity of the rigid body, under a modeling framework of motion of multibody system. In the numerical processing, the three-dimensional rotating angular velocity around the center of gravity can be calculated by a summation of angular momentum generated by external moment and an inertia moment tensor of the rigid body. Effectiveness of the proposed approach has been verified by comparative numerical simulations with experimental waveforms using a test passenger vehicle.