The paper proposes a new modeling method for elastic vehicles. While the vehicle designed lightly to improve fuel economy, it becomes flexible in nature. For obtaining the riding comfort of elastic vehicles, there is a necessity to control vibration and motion. For vibration control, the deformation of the vehicle body must be described. Meanwhile, from the viewpoint of vehicle control, the orientation of the body must also be described. Therefore, we need such a vehicle model that can describe the deformation and the orientation simultaneously. So, in this research, 'Extended Reduced Order Physical Model is applied. Using Extended Reduced Order Physical Model, the mechanical model of the body can be obtained. Then, the equations of motion of the experimental system are derived using multibody dynamics and its linearization is performed. Consequently, the active suspension control is introduced for vibration control. Effectiveness of the control is demonstrated by simulation.