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In the paper, the results of simulation investigations on the application of a semi-active vibration eliminator for suppression of machining chatter are presented. First, the idea of a semi-active vibration eliminator arranged in the "machine tool – cutting process" system (MT–CP) is presented. Next, the results of the identification process of parameters of this system are shown. Properties of the mass-damping-spring system of the machine tool were estimated during the modal testing. A mechanistic model of the cutting process was built on the basis of results of cutting tests. Two control algorithms have been tested: one with the time-invariant model of disturbances (MD) and another with the adaptive model of disturbances. Estimation of the eliminator effectiveness in the suppression of self-excited vibrations in a MT–CP system is also included.