High speed competition vehicles are required to cover a determined number of laps in a closed trajectory circuit in a time that is the least possible, in the limits of the governing dynamic and driving characteristics of these vehicles. Optimization is a methodology that can be used in order to simulate trajectories and driving techniques of used by the competition pilots and to investigate the effects of several parameters in limit conditions of car stability. In this work it is first presented the development of the vehicle model considering the sufficient characteristics for trajectory analysis, influenced by pertinent geometric and physical parameters. In continuation, the problem of the optimal trajectory is defined using optimization procedures, in order to determine how a vehicle will follow the path, considering as an objective function the time to follow it, that must be the minimum, and having as constraints the vehicle dynamic conditions and the path geometry, implementing routines that are used with the Matlab´s Optimization Toolbox. Finally the behavior of the vehicle is presented, represented by the model developed previously in a trajectory control loop, in such a way to compare the resulting behavior with the one predicted by the optimization procedure.