The metallic cables are used for various applications in many industrial fields, such as the aircraft industry, the systems of lifting, the electric lines… In addition, according to the application considered and the conditions of use, the metallic cables undergo degradations whose direct consequences are the strong modifications of the geometrical and mechanical characteristics of the components. What induces a notable reduction of the resistant capacity of the cable according to time, able to bring to failure. In particular at the time of the cyclic requests of loading and unloading where the cable undergoes a phenomenon of tiredness. For safety reasons and an optimal use, it is important to anticipate any brutal rupture. Our work consists in finding a method which allows the optimization of the critical damage and the prediction of its useful life expectancy to be able to change it at convenient time. An analysis making it possible to evaluate the effect of the factors affecting the performance of the long-term cable constitutes the principal work in our lab. It consists in developing a modelling making it possible to envisage the capacity resistant of a cable to various levels of damage of its components, the estimate of the residual life expectancy, the evaluation of the risk of rupture for a level of request given, a mechanical model describing the state of damage by tiredness and another mathematics describing the reliability and finally to an analytical modeling of the relation Damage-Reliability to predict the phenomenon of tiredness of the hoisting cables. The adopted approach is an approach multi-scales with a total decoupling between the scale of the wire and that of the cable. The criterion of the failure in fatigue for the cable is more complex than that applied to the continuous structures, where the measures of length of the crack or a simple observation of the loss of integrity can be enough. These criteria are based on a mixture of former experiment, personal preferences, and of damage, for each particular type of application of cable. The occurrence of the unacceptable number of the cuts of wire is, by far, the most common action adopted for the evaluation of the damage in fatigue of the cable, which justifies our choice. This relation makes it possible to connect the reliability to the damage through the fraction of life expectancy; this led to associate at each stage of damage corresponding reliability. In fact, the theory of the damage considers that the damage reached its maximum value 1 when there is appearance of a macroscopic crack; but the cable keeps a resistance translated by a no null reliability. The latter becomes it when the cable is completely broken. Optimization by the reliability of the damage is a technique which supports knowledge and a follow-up of the state of an entity requested during time. Thing was being able to have interest for a possible application in industrial maintenance. In this context, this work and other works of the same tendency were worked out to manage to establish the bond between reliability as being a statistical size, and the damage by tiredness observed and caused by the cyclic requests.