This book provides a look at the theory behind the programs engineers use for the computer simulation of nonlinear structural behavior. It establishes the mathematical foundations for the development of computer programs that can predict the behavior of mechanical and structural components. After a thorough but succinct introduction, the book delves into mathematical preliminaries, kinematics, stress and equilibrium. Subsequent sections address hyperelasticity for compressible and incompressible materials, finite element discretization, equation solution and computer implementation. A short appendix extends the kinematics to provide for elasto-plastic deformation. The book supplies user instructions, program description and examples for the FLAGSHYP computer implementation for which the source code is available free on the Internet. Worked examples and exercises complete each chapter, making it an essential source for engineers and researchers.