This paper dealing with the problem of modeling an Electro Power Steering System. We introduce a new position model reference structure composed of two inter-connected models. The first model, is a torque booster stage modeled by an hydraulic-like power steering unit providing the total desired steering torque. The second model is a mechanical model providing the desired drive wheel angle, and including a desired tire/road stiffness. This is a two-part paper, the second part (in the same proceedings) presents the corresponding control design and uses the model presented in this paper as a reference one.