Abstract: The mathematical framework of classical continuum mechanics fails when sovling discontinuity problems caused by cracks. In order to overcome this problem, a numerical prediction method for rail fatigue crack initiation was proposed based on the peridynamic theory. The crack initiation life and position of the rail can be predicted using this method. When there were no fatigue cracks, the correctness and applicability of the peridynamic model were verified by comparison with the results of the classical continuum mechanical model. The effects of three wheel states including full sliding, stick-sliding and frictionless on the fatigue crack initiation of the rail were analyzed. The results showed that during the transition of the wheel state from full sliding to frictionless, the crack initiation position transferred from the surface of the rail to the interior, and the number of load cycles required for crack initiation increased from 0.45×10⁷ to 2.05×10⁷. It can be seen that the rolling-sliding states of the wheel affected the location of crack initiation, and the large tangential contact stress significantly reduced the fatigue crack initiation life of the rail.