In this paper, a detailed 3D tire model is first proposed which includes a rigid rim with thickness, different layers of discretized belt points and a number of tread blocks attached on the area formatted by the neighboring belt points. The parameters of the proposed 3D tire model can be divided into two parts: the stiffness and damping values which only involve the in-plane motion and the stiffness and damping values which involve the out-of-plane motion, i.e. the lateral direction. In this paper, the relations between the in-plane parameters of the 3D tire model and the 2D tire model are given. Based on this relation, it is shown that the 3D tire model can generate exactly the same prediction results as the 2D tire model for tire straight line driving dynamics.