The article presents the physical and mathematical model of agricultural unit together with computer simulation of the dynamics during its movement on the eight-shaped test track. In the study, it was adopted flat, two-wheeled tractor model including, by forces applied to the hitch pin, trailer's impact on the behavior of unit. The study is carried out for future construction of a driver, as to ensure movement's safety of agricultural unit on public roads.The identified model takes into account not only the lateral stiffness of the vehicle's suspension, but also the tires' stiffness. Its implementation uses Matlab environment.