The dynamic performances of the machine tools have decisive influence on the achievable accuracy and productivity of the machining processes. For reducing the unfavourable vibrations of machine tools, a system of multi tuned mass disc dampers (MMD system) is developed in this paper. The simulation model of a portal milling machine is built on its CAD model. Thenceforth, the simulation model is parameterized based on the measured natural frequencies, vibration modes and frequency response functions (FRF) of the portal milling machine. Utilizing the parameterized simulation model, the MMD system is designed, the influence of the tuning errors of the dampers is analysed and the robustness of the MMD system is evaluated. The effectiveness and the robustness of the MMD system is validated through FRF measurements and cutting tests on the portal milling machine.