The paper presents a model to analyze the dynamics of a vehicle with fully independent double-wishbone suspension and anti-roll bar on each axis. The model is programmed in Simulink®Matlab® environment and it is useful to describe the dynamic behavior of the vehicle using for that seven degrees of freedom. In the work we consider the displacements on the vertical axis and rotations at the pitch and roll planes of the vehicle for driving conditions across a road with irregularities (steps, undulating road and inclined ramp), steering, braking, starting, and combinations of the preceding conditions. The main results of the model developed are the kinematic behavior of the vehicle under driving transient conditions (pitch angle, roll angle, and accelerations); furthermore, it is found the forces exerted by the suspension system components, the load transfers that occur between the tires due to maneuvers and the accelerations experienced by the occupant of the vehicle while driving.