In this paper, a method for predicting the evolution of fatigue deterioration of structural components using continuum mechanics numerical simulation is presented. At a first stage, prediction will be limited to the evaluation of the end of the initiation phase of the fatigue process. The method is intended for cases where the loading history demonstrates certain repetitiveness (as it is the case for railway traffic induced loading) and is based on the characterization of the deterioration potential of these loading histories by means of the physical quantity of generated entropy per generalized loading cycle. The basic steps towards the development of this method are also presented. At the end, an example of application on a simple reinforced concrete railway underpass is outlined and the expected benefits of the application of this method are explained.