The vibrations of the main spindle of the M/C tools are most important in the consideration of the dymamic performance of the M/C tools. In order to resolve and predict the dynamic behaviour of the main syindle it is necessary to have the mathematical model of the system. The system identification is the procedure to provide us with the mathematical model of the procedure of the system identification of the main spindle of the M/C tools to predict the dynamic behaviour of the machine and further to have the basis for the design of M/C tools.