Manufacturing accuracy prediction of metal pipes using CNC systems is a technical difficulty due to the absence of standardized tools for CAD/CAM system manufacturers that allow controlling the operational programming to ensure the required accuracy. This paper proposes the use of digital twin to simulate the machining of mechanical surfaces, allowing the prediction of machining errors across the calculated parameters of the end of the metal pipe cutting cycle, taking into account the influence of changing technological factors. The study presents an experimental mathematical model of metal pipe surface formation, which allows calculating the variable depth of cut in all surface areas during each machining cycle, based on the geometric compliance of the shaft along the path of the metal pipe surface formation. The introduction of the digital twin improves the prediction accuracy during the design of CNC cutting operations. The developed model is based on the simulation of operational processes using mathematical modelling and analytical methods based on fundamental laws of physics, cutting mechanics, and plastic deformation of the metal during the formation of the metal pipe surface. The scientific contribution lies in the development of a numerical twin model of the metal pipe surface, which for the first time takes into account the relationship between cutting accuracy and technological factors. The study provides a new mathematical and methodological basis for modelling mechanical surfaces using digital twinning, which enhances autonomous control in the programming of manufacturing processes and contributes to ensuring the operational accuracy of various mechanical parts.