The tuned mass disc damper (TMDD) can be applied to avoid chatter of machine tools. The effectiveness of the TMDD depends mostly on the tuning accuracy of the natural frequency. In this paper, three finite element models are presented to simulate the vibrations of the TMDDs. The simulated natural frequencies are compared with measured results. The third model solves the problems of the first and the second model and can predict the natural frequencies of the TMDDs with an acceptable error.