Description: The article deals with generation of mathematical models of a vehicle pneumatic tire at straightforward motion on the spe-cific types of deformable bearing surfaces: cohesive (clay, loam), running (sand, loamy sand) and snow. The comparative analy-sis of known studies as for formation of mobility and performance of wheeled military automotive equipment (MAE), the actual results of road tests and the adequacy of applied mathematical models on the bearing surfaces allows to establish a fundamental difference in the formation of the latter at scientific schools of Russia, the USA and other NATO countries. The US and other NATO countries scientific schools are characterized by a more predictive approach, with an emphasis on the operational evalua-tion of terrain trafficability and potential speed of movement, while the Russian scientific school. instead, elaborates in more details the thermomechanics of tire interaction with different types of bearing surfaces, and the corresponding empirical depend-encies both on the parameters of the bearing surface and on the sample of MAE. However, the analytical evaluation of the ter-rain crossing capacity of MAE, starting from the stage of vehicle designing and including the practical sphere of choice of routes in off-road conditions, determines the appropriate analog computation and calculation of vehicle wheels interaction with a spe-cific type of a bearing surface. This approach is the basis for further actions as for the constructive synthesis of MAE samples, the appropriate selection of parameters and characteristics of the power drive, the developing of routes and the prediction of the mobility level (potential speeds of movement) in the real operation. Practically, the purpose of the analytical evaluation of the interaction of a tire with a deformable bearing surface is a quantitative assessment of total driving resistance, and, accordingly, the required tractive effort - the parameters and characteristics of a power actuator, on the one hand, and the forces of tire ad-herence with a surface, as the border limit of realization of movement possibility and potential speed in case of a larger value of the coefficient relative to the coefficient of driving resistance on the other hand.
Keywords: tire, vehicle, off-road, driving resistance, traction analog computation and calculation.