In this paper the problem of minimising the fatigue wear of machine parts for conditions of elastic contact and dry sliding friction is investigated. Based on using molecular-mechanical theory the mechanism of fatigue wear is represented as a model of tribo-logical object, of which behavior depends on a set of different variables, constants and performance measures. In order to evaluate the influence of roughness parameters on the total rate of fatigue wear, the performance measures expressed in form of equations for wear intensity, residual stress concentration and part surface penetration have been introduced into the model developed.