The volume describes the main theoretical propositions of the methodology to predict mechanical reliability under conditions of repeated exposure to random extreme loads. The mechanical load process is considered to be a form of a discrete sequence of loads occurring at times that form a random flow. The authors present solved problems of reliability prediction of elements having deterministic or random bearing capacity. A method for the probabilistic justification of safety factors is also developed in the book, providing a predetermined level of reliability of elements and systems for sudden failures during design. It considers the methods of prediction and managing reliability under conditions of using safety devices. The main theoretical results are presented in a form available for practical engineering applications. The book can be used by researchers and as a manual by teachers and graduate students of higher technical educational institutions.