Introduction. External forces from the working implements of tractor units or road construction machines often lead to uncontrollable displacement from a given trajectory. This movement is the sum of controlled movement and uncontrolled displacement (start of moving). The lack of adequate models of displacement (start of movement) is the reason for the insufficient study of uncontrolled movement at the present time. The goal is to build a model of uncontrolled displacement under the action of

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... external force, which allows obtaining the maximum value of the external force, depending on its direction.Materials and methods. The mathematical model of limiting equilibrium is built on the example of a bulldozer unit with a skewed blade. The force factors of the interaction of the mover with the soil included in the model were formed on the basis of the mathematical theory of friction. The model was improved by introducing different coefficients of adhesion in the longitudinal and transverse directions. This made it possible to take into account the anisotropy of the interaction of the propeller with the ground.Results. The hodograph of the limiting shift force was constructed as a result of a numerical experiment. His analysis showed that the shift force is equal to the adhesion limit only in the case of translational shear. In all other cases (instantaneous rotational shear) the value of the ultimate shift force is less than the adhesion limit. Anisotropy further reduces the value of the limiting external shear force and rotates the hodograph towards the lowest friction coefficient.Conclusion. The hodograph allows calculating the value of the limiting shear force and assessing the possibility of an uncontrolled deviation of the machine from a given trajectory. The resulting model will subsequently be used to build a control system for the operation of an unmanned vehicle, taking into account the external influence from the working tools.