Mechanics is the “language” used for describing the mechanical behavior of materials. An understanding of basic constitutive models, such as elasticity and plasticity, is essential for undertaking deformation analyses. In this chapter the fundamental concepts and field equations are reviewed. The contents are limited to topics that are within the scope of this book and are intentionally terse. Readers who seek detailed information on solid mechanics may consult specialized textbooks (e.g., [1–7]). Other relatively brief overviews may also be found in the chapters of Refs. [8–10]. Issues concerning implementation of numerical modeling will also be addressed toward the end of the chapter.