This paper proposes a modeling method for elastic vehicles. Flexiblizing the vehicle body invites a bad influence on a degree of driving comfort or operation stability. In order to improve them, active suspension control is used. Although a model is required in order to control motion and vibration of elastic vehicles, the ordinal modeling was is difficult to apply since an elastic vehicle is in a flexible multibody system. Then, the created elastic vehicle is modeled using the extended reduced physical order model proposed by us that can perform expression of motion and vibration. In derivation of the equations of motion of an elastic vehicle, the additional constraint method is derived. Since linear control theory is used, linearization of the equations of motion of the elastic vehicle expressed by a multibody system with nonlinearty is performed. By changing the equations of motion into state space form, a control system design can be made easy.