Friction and wear process are investigated using experimental data and mathematical modeling of the specimen contact interaction. To study the wear in the system, 'a rigid punch-thin coating-elastic base', a mathematic statement of the problem was formulated. The integral equations were obtained and the solutions to the problems for punches, containing parabolic and wedge-shaped profiles, and also with a flattened basis were constructed. New regularities of deformation and wear of thin coatings on solids were obtained. The methods for crack growth resistance calculations in the coatings allow us to predict by the physicochemical, tribotechnical and geometrical characteristics the coatings life-time, which is proved experimentally on chromium-based coatings applied on carbon steels. (C) 2004 Published by Elsevier Ltd.