Structural elements with low dynamic stiffness are prone to excessive vibrations. A boring bar which is used to make long bores, and which is characterized by large length to diameter ratios, is a typical example. During machining, a boring bar can easily get excited into excessive vibrations called machine tool chatter. In this paper, an active dynamic absorber is considered as a device to be used to actively control the vibrations of the boring bar. A piezoelectric pusher is assumed to be the active element in the dynamic absorber. The boring bar with the active dynamic absorber is modelled using finite elements. Optimal control algorithms are used to calculate the feedback parameters for closed-loop control. Harmonic and transient responses are obtained with and without the feedback control. Results show that the active dynamic absorber is effective in attenuating the level of vibrations.