The final thesis describes the design and manufacture of a dynamically optimized CNC machine. The design itself was developed through initial selection of design solutions using comparison matrices, preliminary static calculations, and modal analysis of natural frequencies of the CNC machine using the finite element method. The purpose of the modal analysis was to increase the critical natural frequencies. By doing that, the vibration amplitudes were decreased, which results in increased quality of machined parts. Since the induced vibration forces were not known due to a great variety of used tools and materials it was possible to optimize the machine only by increasing the lowest natural frequencies. To ensure proper meshing of the machine elements with finite elements some significant simplifications were made in order to ensure stable and fast convergence of the results. The analysis was conducted in stages. In each stage, X, Y, or Z axis subassembly was analyzed. The optimization process resulted in an increase of two X axis's natural frequencies by a factor of 2.1 and 3.1, respectively. Finally, the whole CNC machine was analyzed. The thesis further describes the machine's detailed design, motion control using stepper motors and manufacture.