Fatigue of engineering materials is a very complicated process that is difficult to accurately describe and predict. It is no doubt nowadays, that a fatigue of real materials should be regarded as a random phenomenon and analyzed by use of shastic theory. This volume of the lectures sumarises the latest achievements in shastic modelling and analysis of fatigue. The lectures cover the following important aspects of modern analysis of fatigue: methodology of shastic modelling of fatigue, tools for characterization of random fatigue loads, physical and mechanical aspects of random fatigue, basic shastic models for fatigue and the estimation of fatigue reliability of specific structural systems.