During car races, strong vibrations appear in the chassis of the vehicle, due to the high power created by the engine which are then transmitted and, therefore, affect the driver’s condition. The study of these vibrations is a subject frequently addressed by researchers, analyzing the influence of different parameters on the forces to which the pilot’s body or certain sensitive body parts are subjected. In this paper, we analyze the particular case of a racing car made to meet safety requirements in the event of an accident. For the analysis of the forced vibrations induced by the running track, the finite element method was used. This method proved to be a useful and stable modeling and analysis method, validated by practical applications. A standard-equipped racing car with a mannequin inside was studied. Once the natural frequencies of the structure were determined, the response of some points of the mannequin’s body to the movement caused by the running track or the engine was analyzed. Modeling and discretization were performed using well-known classical procedures. The obtained results revealed the parameters that can negatively influence the body of the mannequin which were communicated to the design team. The conclusion of this study is a racing car that was successfully used in Formula Student competitions.