The development of wear maps has enhanced a new approach to the wear behaviour of materials as it is a precise description of the mechanical loading (local stress and strain fields). This paper studies crack nucleation using fatigue criteria in the case of an elastically loaded dry contact. Fretting behaviour is analysed for partial slip conditions which have been identified experimentally and theoretically (transition criteria developed using Mindlin's analysis). A Dang Van crack nucleation criterion is introduced for a ball-flat contact. Typical analytical expressions of the criterion were obtained on the surface and in the volume depending on the loading conditions and the contact system. They are expressed as a function of the mechanical properties, the friction coefficient, the contact geometries and the fatigue limits under both shear and tensile loadings of the material. The results obtained permit the investigation of the position and the direction of the first crack created by fretting conditions.