This book gathers the presentation made during the Advanced Research Workshop held in Portoroz (Slovenia) in October 2008, under the auspices of NATO Science for Peace and Security Programme. It is edited by Professor Guy Pluvinage from the University Paul Verlaine – Metz (France) and Professor Aleksandar Sedmak from the University of Belgrade, Faculty of Mechanical Engineering. Both have a long and rich experience in analysis of theoretical and practical cases in safety and reliability of structures. Other contributors are all known as experts in the areas of fatigue, facture and reliability of structures.