Elasticity, plasticity, damage mechanics and cracking are all phenomena that determine the resistance of solids to deformation and fracture. The authors of this book discuss a modern method of mathematically modeling the behavior of macroscopic volume elements. The first three chapters review physical mechanisms at the microstructural level, thermodynamics of irreversible processes, mechanics of continuous media, and the classification of the behavior of solids. The rest of the book is devoted to the modeling of different types of material behavior. 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.