Introduction. Integrated automation of production processes is the main achievement of scientific and technological progress. The creation and use of flexible production modules and production complexes for material processing by cutting leads to the acquisition and mass use of numerical control machines (CNC). Also at the same time, there is a trend of obsolescence of the machine stock of enterprises and a decrease in the initial quality of this equipment, therefore, the actual task is to ensure and improve the quality of the products produced while simultaneously reducing their cost. The aim of the work is to increase the effectiveness of technological processes in turning machining on machines with numerical program control due to mathematical and finite element modeling. In this work, the stress-deformed state of a part in the software product Solid Works Simulation from the effects of cutting forces and on the basis of mathematical modeling were carried out taking into account the strain deviations, a transformable CAD model of the work piece was obtained and a control program for this machine was developed for this model. When performing the work, the following research methods were used: methods of computational mathematics, mathematical modeling, matrix analysis, statistical processing of experimental results. Experimental studies were carried out using CAD / CAM system Solid Works Simulation, turning center SMTCL CAK50135, coordinate measuring machine. The article presents a method of controlling the geometric accuracy of parts machined on CNC machines based on mathematical and finite element modeling. The control of the geometry of the parts is made according to the CAD model that characterizes the reference part. Results and Discussion. When processing two batches of blanks, the first of which was processed according to the traditional method, the second according to the offer, and determining the reliability of the technological operation, it was noted that the dispersion field of real values and the standard deviation decreased according to the proposed method, which confirms its effectiveness, since the percentage of probabilistic marriage is significantly reduced. Moreover, the developed model of geometric accuracy control of details, based on mathematical and finite element modeling, also contributes to the reduction of the main technological processing time by eliminating additional refining passes of the cutting tool.