We propose an analytical model for investigation of the processes of fracture of a near-surface layer of bodies in the case of their unidirectional rolling under conditions of limit lubrication. The step-by-step calculation of trajectories of propagation of fatigue cracks using the criteria of local fracture in a complicated stressed state and with regard for the specific features of loading in a contact cycle is a key element of the model. We investigate trajectories of propagation of an edge crack depending on the angle of its initial inclination to the boundary of the body, the friction coefficient between the contacting bodies, and the pressure of lubricant on the crack lips. The theoretical results confirm the experimental data and the known hypothesis of Way, according to which a lubricant plays the decisive role in the appearance of a pit.