This work shows the development of a full vehicle model for the Reptiles Baja PUC-Rio Team prototype, with the intension to offer to the team a powerful tool for optimization and development of Baja SAE Competitions vehicles. The mathematical model is developed using the kinematic chain methodology, or multibodies, for this uses SimMechnics, a tool offer by the software MATLAB, in interaction with the models of the vehicle subsystems, as shock absorbers, tires, brakes and power-train, those are developed in Simulink, a MATLAB dynamics systems simulation tool. The main target of the mathematical model is to analyse the steering and suspension dynamic of the prototype in similar conditions of the Baja SAE competitions, thus, the power train, breaks, and aerodynamic models are simplified. The vehicle shock absorbers works with an air spring and a fluid dumping, for such, is developed a thermodynamic model, that is validate by traction tests. Because of the diversity of the obstacles in the Baja SAE competitions, is developed a three-dimensional tire model, capable of simulate the interaction with several types of obstacles, an for the fiction force calculations, the Pacejka Magic Formula is applied.