Based on the ordinary state-based peridynamics (OSB PD) theory, a 2.5-dimensional (2.5D) PD model for rail crack propagation in railway turnouts was proposed. First, a two-dimensional (2D) model for rail crack propagation in railway turnouts was constructed, with two types of 2.5D additional constraints for crack opening and cross section proposed on the basis of the 2D model. The 2.5D PD model for rail crack propagation in railway turnouts could thus be established. A fatigue crack propagation experiment was subsequently carried out on the U71Mn turnout rail material. The bond fatigue failure condition of the turnout rail material was established on the basis of the experimental results. Finally, the accuracy of the structural deformation and bond fatigue failure conditions was verified. The simulation results for rail crack propagation were compared with field observations and then analyzed in detail. These results show that the proposed 2.5D PD model can be used to accurately simulate the characteristics and rules for rail crack propagation in railway turnouts.