This textbook gives a concise survey of constitutive and structural modeling for high temperature creep, damage, low – cycle fatigue and other inelastic conditions. The book shows the creep and continuum damage mechanics as rapidly developing discipline which interlinks the material science foundations, the constitutive modeling and computer simulation application to analysis and design of simple engineering components. It is addressed to young researchers and scientists working in the field of mechanics of inelastic, time-dependent materials and structures, as well as to PhD students in computational mechanics, material sciences, mechanical and civil engineering.