This book provides a comprehensive introduction to load-strength-durability models for reliability analysis of loaded composite structures with components with internal flaws. It is essential reading for lecturers and graduate students involved in reliability engineering, practicing engineers, researchers and consultants dealing with strength and fatigue life of composite structures. It is an useful tool also for lecturers in applied probability and statistics. Through a number of practical applications and case studies the book gives examples of using the Markov chains theory and basic Monte Carlo simulation techniques for solving reliability engineering problems. Some examples can be considered as a base for a graduate works of graduate students. It is assumed that the reader has a modest acquaintance with probability theory, Markov chains theory, mathematical statistics, and is familiar with the basic ideas of reliability theory.