The article suggests defining the pattern of the interaction between the support base and the wheel of the transport vehicle by means of the Gilbert - Johnson - Keerthi polyhedra intersection algorithm that allows examining the wheeled vehicle’s crossing the obstacles of any profile, including the ones with the vertical walls and negative grades. With the view of the simplicity and the computations efficiency increase the suggested technique is restricted by the two-dimensional interaction between the circle of the wheel and the polygon of the road. The article provides the dependencies necessary for finding the forces and torques arising during the interaction between the wheel and the supporting surface. We introduce a simulated computer model, used for the suggested technique. The patterns of simulating the wheeled vehicle motion over the various supporting surfaces are considered. We give recommendations regarding the use of this technique for solving the spatial problem of investigating the profile passability.