The quality of the part is characterized by precision of its processing. A good fit of the product parts and, as a consequence, its reliability in general depends on how accurately the size and shape of the part is maintained during machining. In this connection, the article considers the problem of ensuring the accuracy during machining of work pieces using CNC machines. Within the identified problem, the analysis of known technical solutions in this area was carried out and three main areas were identified: optimization of cutting conditions, improvement of the treated surface area according to the criteria for increasing the resistance of the cutting tool, as well as error tracking and correction during machining. The main disadvantages of the analyzed methods and inventions are complexity of their implementation, the need to equip the CNC machine with an adaptive control system, and a limited field of application. Therefore, a method for controlling the accuracy of shaft processing using mathematical and finite element modeling is proposed.