Abstract: The probabilistic models for the random fatigue stress-life relations of LZ50 axle steel are investigated. The models consist of the survival probability-stress-life curves, the confidence stress-life curves and the confidence-survival probability-stress-life curves. These curves are estimated by a so-called “general maximum likelihood method”. Standpoint of the method is using the randomness of entire stress-life data to characterize the models, rather than using that of local data as in the conventional methods. Effectiveness of the models and feasibility of the present method are verified by an analysis of the present test stress-life data.