The possibility for using a viscoelastic material for the vibration absorber instead of conventional spring and viscous damper is studied in this thesis. For this, dynamic elastic modulus and loss factor of a viscoelastic material are obtained as functions of frequency, temperature, and prestrain. With these properties, optimum tuning and damping ratio of the absorber are obtained by adjusting the geometrical shape of the damper and the magnitude of prestrain in such a way that the vibration of the primary system could be most efficiently suppressed. It is shown that the viscoelastic vibration absorber has better capability in reducing vibration of the primary system compared with the conventional springviscous damper-vibration absorber. Also the viscoelastic vibration absorber shows applicability to the case where the natural frequency of the main structure is not fixed, but changing, because the optimum tuning and damping ratio of a given absorber can be achieved to some extent just by adjusting the prestrain without changing the absorber itself. From this and other aspects to be explained later the viscoelastic vibration absorber is believed to be superior to the absorbers hitherto used.