The discrepancy between the plow width and the tractor width leads to the asymmetry of plowing units. The geometry of the plowshare surface of the moldboard plow contributes to the generation of lateral forces on the working tool. All this leads to the imbalance of the tool and the deviation of the tractor from straight-line movement during plowing. To maintain straight-line movement, the driver has to adjust the machine every 5-10 meters, which is highly tiresome. To study the causes of lateral slips of the plowing unit, we constructed a mathematical model, which consists of the equations of controlled movement and equations of the tractor's uncontrolled shear under the action of external forces from the plow. The description of the force interaction of the drive with the ground is based on the mathematical theory of friction, taking into account anisotropy and elastic properties in contact. Based on the passive shear model, we constructed a hodograph diagram of the maximum tractor shear force from the side of the working tool. We found that the shear force reaches its maximum friction value only in the case of a translational shear, when its line of action passes through the tractor's center of gravity. In all other cases, the shift (slip) of the tractor is caused by a lower force. We formulated the features and assumptions of the model as applied to caterpillar and wheeled tractors. As a result, we found that, regardless of the direction of the lateral displacement of the plow's traction resistance, the tractor is slipped towards the plowed field. The result of the numerical experiment showed that the main reason for the slip of the wheeled plowing unit is the difference in soils along the sides of the tractor but not the deviation of the plow traction resistance.