Mathematical models of gear coupling failures on the criteria of strength and the wear resistance of tooth materials have been developed. The failure models are based on the mathematical dependencies of the reliability theory of machine parts, the basic kinetic concept equation of the material structure damageability and the thermodynamic strength condition of solids, as well as the determinant dependencies of the energy-mechanical concept of stationary tribounit wear. An algorithm and the «Durability of gear couplings» program have been developed to implement the created models that allow one to estimate the average expected service life under the specified operating conditions and identify the most durable design options based on a theoretical analysis of the technological and design parameter influence on the design service life.