Elasticity, plasticity, damage mechanics and cracking are all phenomena which determine the resistance of solids to deformation and fracture. The authors of this book discuss a modern method of mathematically modelling the behaviour of macroscopic volume elements. The book is self-contained and the first three chapters review physical mechanisms at the microstructural level, thermodynamics of irreversible processes, mechanics of continuous media, and the classification of the behaviour of solids. The rest of the book is devoted to the modelling of different types of material behaviour. In each case the authors present characteristic data for numerous materials, and discuss the physics underlying the phenomena together with methods for the numerical analysis of the resulting equations.