Abstract: A probabilistic model is established for the random propagation of fatigue long crack on the basis of Elber-type equation.The concept of effective stress intensity factor range is extended as stress intensity factor range minus its threshold.The effects on probabilistic assessments due to the scattering regularity of test data and sampling size are considered.The model is mainly comprised of the survival probability-based curves,the confidence-based curves,and the survival probability-and confidence-based curves.Parameters of the model are measured by a linear regression technique and a maximum likelihood method.The test data of LZ50 axle steel for the Chinese railway vehicles are used to validate the availability and feasibility of the model.It is found that the model can give good prediction from threshold to mid-and high-range of the stress intensity factor.