The basic problem in material research is to predict lifetime behaviour of structures [
]. That is not only a material problem, but also loading conditions, technology design and environmental properties are very significant [
]. A service loading has usually a random character. Traditional experimental investigation methods are very expensive and time-consuming in this case. Therefore, a computer-simulation method seems to be a very suitable way to this purpose. In order to evaluate fatigue damage under dynamic loading, the cumulative representation of a damage increase over a closed cycle is accepted [
]. Under a harmonic loading with constant both amplitudes and mean values of cycles, stress-life (σ-N) and/or strain-life (ε-N) curves can be experimentally obtained. Then it is possible to specify a relative damage over a closed loading cycle according to some hypothesis (e.g. Miner, Corten-Dolan, etc.) [
]. The difficulties arise under varying mean value of cycles because the relative damage accumulated over individual cycles cannot be simply added. The complete loading history must be respected, and it is a big problem especially under random loading.