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Residual strength is usually used to characterize the degradation rule of material performance under the cyclic load,which is critical to fatigue life prediction as well as reliability assessment of materials.In order to reveal the probability characteristics of residual strength of material under uncertain cyclic load,the relationship between extal stress and fatigue life (i.e.,the equation of S-N curve) is considered in this study.Firstly,the probability density function of fatigue life under uncertain cyclic load is derived from the probability density function of extal stress.Then,a probability model of residual strength is proposed on the basis of a fundamental assumption that the residual strength and the remaining life of material depend on the same damage state.Finally,the validity of the proposed model is verified by an illustrative example.The results indicate that the probability distribution of residual strength of material is affected by both the extal factor (i.e.,probability characteristics of the load) and the intal factor (i.e.,fatigue performance parameters of material).