Without understanding the nature and mechanisms of an elasticity and the effect of various factors on internal friction, it is difficult to solve the problems of using internal friction measurement for evaluating the structural stability of alloys, cyclic microplasticity and for better understanding the processes associated with the response of materials to single or repeated loading. The author presents important new results for the relationship between internal friction and the defect of the elasticity modulus with many principal processes such as plastic deformation, effect of temperature of plastic deformation, effects on the structural stability of alloys and composites up to cyclic microplasticity. The existence of critical strain amplitudes is discussed and supported by experiments, and attention is given to the link of cyclic microplasticity with dislocation density and activation volume of plastic deformation up to the effect of individual factors on the cyclic plastic response of the material. The relationship of the process of mechanical fatigue of the material with internal friction and the defect of the elasticity modulus is discussed. The author proposes a new fatigue life equation which has been verified by a large number of experiments.