Abstract. The article discusses the problem of increasing the accuracy of machining workpieces on machines with computer numerical control. Within the framework of the problem identified, the role of the finite element method for solving it is considered. Moreover, numerical simulation is primarily used for receiving estimates of operational and technological characteristics of the developed product, and in the present work we propose to use a method of the finite element analysis as a tool for ensuring the accuracy of shaping the surface of a workpiece in process systems for determining the deformation of the workpiece under the action of cutting forces and transformation of its geometric shape prior to direct machining based on identified deviations. That is, the possibility of applying the finite element method in the development of control programs for details such as bodies of revolution is considered.