Introduction. A relevant objective of implementing the advanced systems of self-driving road construction vehicles can be accomplished by mathematical modelling. One of the important issues when creating a motion control system for a self-driving vehicle is to develop a trajectory following algorithm. The most well-known method of following the trajectory is a pure pursuit method, which is successfully used to control the movement of mobile robots.Materials and methods. Hence, the research objective has been defined and is to adapt the pure pursuit method to control an autonomous grader. To achieve the research objective, the task of a mathematical model of the motor grader movement with front steering wheels has been developed, and a mathematical model of the motor grader motion control system has been compiled. Besides, we propose an integral criterion to evaluate the efficiency of the motion control system of a unmanned grader. Some theoretical studies of the mathematical model have been carried out and the dependencies of the integral criterion on the design and operational parameters of the grader, as well as on the parameter of the control method (visibility range) have been obtained. Moreover, the optimal values of the visibility range for various values of the base length, base coefficient and machine speed have been defined according to the proposed efficiency criterion.Results. As a result of approximating the obtained optimal values, the pure pursuit method has been modified to control a self-driving motor grader, taking into account its design features and travel speed. The results obtained can be used to create the prototypes of unmanned control systems for road construction vehicles.