A new history-dependent phenomenological model of cumulative damage is presented. It is a stochastic model. The model includes as an inherent part of its structure the major sources of variability encountered in fatigue and wear. The generality possessed by the model is much more in accord with the complexity of fatigue and wear processes than possessed by models in current use. It also implies that the frequent inaccuracies encountered in life prediction when using current models are not surprising and cannot be substantially reduced using such models.