Abstract: In this paper, the randomness of fatigue loading, fatigue stress, fatigue life and fatigue strength are clearly classified. Then, typical accumulative damage rules developed in the history of fatigue theory and still employed currently are systematically analysed according to the mechanism of mechanics-probability and the usage range. Two different probabilistic interpretations about fatigue damage accumulation, i.e., the stochastic nature of damage developed in a single individual and the scatter of damage...