The basic indicators of damping intensity are: damping decrement, specific damping coefficient, quality factor and phase shift angle. The main purpose of clutches connecting an engine with the rest of the elements of a machine is to transfer and mitigate disturbances of torque as well as to damp vibration of the elements through energy dissipation. The problem of deriving a precise mathematical description of structural friction is very complicated because of the complexity of friction phenomena as well as difficulties in describing the stress or strain states present in the slip zone. Most commonly, the mathematical description is based on many simplifications. The optimum value of the pressure grows with decreasing friction coefficient. The proper design of a clutch should take into account the pressure which is appropriate to the maximum torque to be transferred and the possibly high vibration damping level.