A general notion of the cumulative damage is introduced which accounts for the previous damage history and loading order effect. The dimensionless damage is specified in terms of a damage function containing a controlling damage variable, ψ, and material parameter, p. This nonlinear damage accumulation model is based on the phenomenological approach which relates the rate of increase of damage to that of cyclic loading through the damage function. Specific forms of the damage function are discussed with reference to earlier investigations. A particular form of the damage function is the logarithm of the strain energy per cycle which correlates well with the multi-step loading in both low- and high-cycle regimes