Vibration damping is one of the manifestations of the dissipation of mechanical energy related to motion in mechanical systems. Damping processes have been studied for a long time. The development of research on problems related to vibration entails studying its damping. Admittedly, those studies lag behind other aspects of the investigation of vibrating motion. Low damping prolongs the free vibration, so disturbances in the performance of a machine last longer. At the same time the number of loading cycles increases, which results in quicker appearance of a fatigue fracture. The role of damping is very important in machine dynamics. Quite often designers decide to incorporate special dampers to their constructions. It makes the projects more costly and the dampers themselves become an additional source of technical problems. It requires, a good knowledge of vibration damping phenomena as well as energy dissipation mechanisms affecting the vibration.