Introduction. The paper discusses the methods of processing large parts having curved convex surfaces with a rectilinear guide on multi-coordinate CNC machining centers using the touch method with a discrete motion of the tool feed along the profile of the part. It is shown that the main disadvantages of this method are lower productivity, which is due to the presence of discrete tool motions between cycles of its translation mode, where the value of discrete tool motion for a given processing accuracy depends on the curvature of the surface being processed. To improve processing performance, it is proposed to use prefabricated disc cutters equipped with replaceable polyhedral inserts (RPI) with rectilinear cutting edges. Its installation in the cutter body with non-zero angles of inclination of the main cutting edge, in combination with an additional rotation of the cutter, during processing, along the direction of the translational feed movement, allows you to obtain a concave surface and ensure a tighter fit of the producing surface of the tool and the machined surface of the part. The aim of the work is to reduce the error of approximation of the profile when it is processed using the touch method with discrete motion of prefabricated disc cutters along the profile and, consequently, to ensure workpiece the possibility of increasing the step of tool movement along the profile being formed to improve processing performance. Research methods: geometrical theory of designing metal-cutting tools. Results and discussion. The regularities established in the work made it possible to create a method for determining the angle of inclination of the main cutting edge of the RPI milling cutter and the angles of rotation of the milling cutter along the direction of translational feed movement during line-by-line processing of extended sections of parts with a curved profile on multi-coordinate CNC machines by turning the milling cutter to ensure the best fit of its producing surface to the surface being processed at the point of its contact, to reduce the approximation error processed profile and improve processing performance, due to the possibility of increasing the tool movement step.