An original method for steady, linear, mechanical closed loop system vibration analysis is presented in the paper. The finite element method, the abilities of which are extended, including the coupling element term, is applied to modelling. The problem of excited periodic vibration has been formulated and resolved numerically using the Fast Fourier Transform (FFT) for this purpose. An illustrative example is presented using a computer model of a real milling machine to consider stationary cutting conditions. Some comparative calculations for various types of feedback interaction are performed and time plots for steady-state vibration are obtained.