Abstract: Fiber-bridging effect has significant influnce on the crack growth of fiber reinforced matrix composites.A first crossing diffusive process stochastic model of fiber-bridging fatigue crack growth was established on account of statistical characteristics of related data of the fiber-bridging fatigue crack.First,based on Paris law,the material inhomogeneity and loads randomicity were considered,the fiber-bridging fatigue crack growth process was assumed to be a diffusive Markov process and the stochastic averaging method was employed to establish the FPK equation with the transition probability function satisfied.Second,the differential equation,of which the kth order conditional moment of the first crossing fatigue crack growth time is satisfied, was established and the kth order conditional moment was solved.From the numerical results,the established stochastic model is comparatively effective for simulating the fiber-bridging effect.