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Practice shows that with insufficiently high traction qualities of traction vehicles deteriorate its operational properties. At present, extensive research is under way at home and abroad to find inexpensive but highly effective ways and techniques to improve the traction qualities of vehicles. The design of running systems with reduced resistance to movement and slipping will help to significantly increase the productivity of vehicles and reduce fuel consumption. This, in turn, will contribute to greater operational efficiency for traction vehicles. The authors of this study have developed the design of a traction vehicle with a half-tracked propulsor. The objective of the study is to develop a mathematical model for calculating the efficiency of operating a traction vehicle equipped with a half-tracked propulsior with rubber tracks. The proposed mathematical expression takes into account the deformability of the rubber tracks of the propulsor, the uneven distribution of normal pressure along the length of the track, slipping, geometric parameters of the propulsor and the physical and mechanical properties of the soil. Using numerical methods, calculations were carried out to determine the effect of the tangential tractive force on the slipping of a wheeled traction vehicle with a different layout of the running system. The dependences of the amount of slipping on the tangential thrust force are determined. It has been found that with an increase in the traction force, the slipping increases, however, the intensity of growth of a half-tracked propulsor compared to a wheeled propulsor is much lower.