This book offers a state-of-the-art overview and includes recent developments of various direct computational analysis methods. It is based on recently developed and widely employed numerical procedures for limit and shakedown analysis of structures and their extensions to a wide range of physical problems relevant to the design of materials and structural components. The book can be used as a complementary text for advanced academic courses on computational mechanics, structural mechanics,  soil mechanics and computational plasticity and it can be used a research text.