Traffic accidents can have more or less dramatic consequences that involve penal and civil responsibility with amplitude extending over long periods of time. In many cases, substitution of the driver with the passenger in order to avoid criminal responsibility is often remarked. The substitution takes place with the passenger's agreement or, in cases with dramatic consequences (coma or death), without his/her consent. These situations are encountered in civil cases regarding insurance fraud. In addition to forensic medical expertise, to aid the experts, mathematical modeling and computer simulation of the dynamics of vehicle passengers is a tool that completes the criminal expertise of traffic accidents. This paper presents the method of identification of the person driving the vehicle based on the computer simulation of vehicle occupants' dynamics.