We designed and successfully manufactured a complex experimental piece composed of surfaces with zero, positive and negative curvatures. We planned and executed the machining manufacturing process by using milling process with end ball nose tools on a vertical machining center equipped with a fourth external rotational axis. For planning, simulation and verification of the machining process, we developed a virtual model of the machine tool and its accessories in a commercial system for computer aided machining. By mounting the virtual manufacturing system, we verified the process and adjusted it until observe a good performance. We tested and confirmed the advantages of using the recent virtual methods for simulation and verification of the process offered by various computer-aided machining systems, especially when dealing with complex processing components in machine tools with more than three axes.