For the construction of automobiles intended for off-road and cross-country driving and the evaluation of their characteristics from the viewpoint of cross-country capacity it is necessary to know the relations between the parameters of the vehicle and its abilities to overcome principal types of terrain obstacles. Till now, the problem was investigated only under the conditions of very slow driving of the vehicle, neglecting the effect of inertial forces and kinetic energy and the published data are not in mutual correspondence.Stated in this paper are the results of complex analysis of the step-obstacle performance of a two-axle vehicle and the used method of analysis which can be applied also to other shapes of obstacles. The derived relations for the "static" step-obstacle performance, when neglecting the effect of inertial forces, show that this step-obstacle performance depends on the adhesion and on the dimensional parameters of the automobile, which are the radius of its wheels, wheel base of axles and longitudinal and height coordinate of the centre of gravity. For practical verification of the validity of derived relations was selected the method of test runs with reduced model of vehicles, having variable parameters. A portion of tests was executed with actual vehicles. In the course of these tests it is important to pay attention to the value of the coefficient of adhesion and to process correctly the results of the measurements.