Abstract: The effect of the residual compressive stress in the overload plastic zone is equivalent to an effective stress σr, and as proposed by WillenborgwhereIn the present paper it is further assumed that σr is not constant during one baseline cycle, but it varies from σr at σb max to ασr at σb min , α is a relaxation factor. Thenso the effective stress range （△σb）eff during the baseline cycle isOr alternatively the above equation may be written in the following formIt is easy to show that the maximum value of Kap during the transient period following the overload will be where the overload ratioMany investigators have found that when the overload rate increases to some critical value ra, the crack will cease to propagate at all after the overload. It is reasonable to assume that when r reaches ra, （△Kb）eff min will decrease to a value （△Ab）eff min = △Kth, so the crack will cease to propagate. Using this condition, we getorIf the crack propagation rate is expressed by Paris formulathen the reduced rate of crack propagation following an overload will bethe unretarded rate of crack propagation correspondingto （△Kb）.The retarded number of cycle ND can be calculated bywhere △aa is the length of the retarded zone.The retarded number of cycle of some specimens of LY12, 2024,7075 aluminium alloys, Ti-6Al-4V titanium alloy and a stiffened plate under different loading conditions are predicted by the present method. By putting the coefficient n = 4 , we find that the agreement between the predicted values and the tested values is good, as shown in fig. 2 of this paper.