1. For machine parts with stress concentrators and residual compressive stresses in the surface the conditions were determined in which fracture shifts from the concentrator to the smooth surface. 2. To prevent fracture in the concentrator it is necessary to increase the residual compressive stresses and increase their concentration so that the depth of residual compressive stresses corresponds to the dimensions of the concentrator. 3. It is necessary to select methods of creating residual compressive stresses on the surface that ensure small stress gradients at depths comparable with the dimensions of the concentrator.