The process of fatigue fracture of carbon fibres reinforced plastic under compressive loads is considered from the standpoint of the theory of reaction rates.Numerical simulation is based on rheological structural models of Wallet the material, which reproduce thermodynamic processes of local plastic deformation and failure occurring in time.The prediction of longevity of composite materials under compressive loads is similar to the solution of the problem for metal alloys under tensile loads when temperature and girls dress stresses are arbitrary functions of time.