"In recent years, the use of composites and nanocomposites in various aerospace, automotive, marine, and civil engineering applications has been constantly increasing. Without exaggeration, it can be said that it is among the most complex and urgent problems of the mechanics of a deformable solid, since a number of specific phenomena and difficultly taken into account analytic factors arise during cyclic loading. They are primarily associated with the development of fatigue damage, with the need to assess the cyclic and structural instability of composite and nanocomposite materials. Currently, the problem of structural strength under cyclic loading is considered much more widely. This is due to the development of new industries in modern technology, such as aircraft, power engineering, aviation and rocket technology. The cyclic loading significantly reduces the creep resistance in the entire frequency range, and it became obvious that such traditional characteristics of strength as endurance limit, static creep limits and long-term static strength can no longer suffice the design criteria for reliable performance. As a result, new directions appeared in the section of high-temperature strength - cyclical creep and long-term cyclic strength. These circumstances led to the creation of new methods and means of determining the resistance of composites and nanocomposites materials and continuum damage development under cyclic loading; to the creation of appropriate physical models. Particularly relevant is the intensification of creep by high-frequency cyclic loading in composite materials, which usually occurs at high temperatures. Most of the known studies in the field of cyclic creep are experimental, and the direct use of number of cycles to define damage model cannot escape the empirical relation that predicts multi-stress level fatigue life well"--