The primary focus of this work was the calculation and construction of the „Z“ axis of the CNC milling machine. According to the order of the task, the introduction describes the history and the present of CNC machines in general and their classification, overview of CNC milling machines specifically, and some differences in the CNC milling performance. The next chapter describes the „Z“ axis of the CNC milling machine with respect to the selection of individual parts and depending on the parameters that are to be met. Thereafter, it follows the chapter in which detailed calculation of the forces and velocities is given for the various types of milling. The tool selection was initially carried out for each individual milling operation, on which the calculation was based, and the data was obtained from the manufacturer. By selecting standard components, the theoretical part of the work was completed and the data obtained was used for the purpose of constructing the 3D model of the „Z“ axis of the CNC milling machine in Autodesk Inventor. Based on the constructed 3D model, worksheets were drawn using the Autodesk Inventor and AutoCAD software, which are found in the attachment.