In the Doctoral Thesis a new mathematical model for wear calculation and analysis is developed to determine the wear of sliding friction pairs, including surface texture (3D) parameters, deformation mode and stress parameters in the case of fatigue wear. A new contact model of the friction surfaces and a new methodology for calculating the lifetime of a friction pair have been developed. A validation of the results of the new mathematical model of the wear of friction pairs was carried out. The correlation of the experimental wear values with the analytical calculations was analysed. The synthesised friction surface wear calculation model allows the wear values to be determined analytically and the wear parameters to be analysed and optimised during the design process.