Abstract: A statistical model of fatigue crack propagation under r andom loading is proposed. The uncertainties of material resistance and applied loading are introduced into the deterministic fatigue crack growth rate in the strain energy density factor range, and the fatigue crack size is approximated by a diffusive Markov process. The backward Fokker–Plank equation, which the transition probability function of crack growth process satisfies, is derived from the stochastic averaging method. The associated boundary conditions are derived. The distribution of crack growth time with given crack size is obtained using Eigenfunction method. The sought distribution function is expressed in the form of a convergent infinite series. An example is given, in which the probability density function of crack growth lifetime is calculated.