This book provides a comprehensive description of the major methodologies of nonlinear finite element analysis for solid mechanics, as applied to continua and structures. Treatment of the subject is integrated in such a way that the reader can gain an understanding of the fundamental methods, a feeling for the comparative usefulness of different approaches and an appreciation of the difficulties inherent in nonlinear analysis. In-depth coverage of the following is given:Lagrangian and arbitrary Lagrangian Eulerian treatments of continuamany of the material laws used in todays software and researchsolution methods, including explicit and implicit time integration methods and methods for equilibrium problemsbasic concepts such as stability and smoothness, and techniques such as linearization and regularizationmethods for shells and structurescontact-impact problemselement technology, including multi-field elementsIdeal for self-study, no other book provides such a comprehensive description of nonlinear finite element analysis for solid mechanics. This is an invaluable reference not only for final year undergraduates, postgraduates, academics and engineers working on sophisticated finite element software and in the field of solid mechanics, but also for all users of nonlinear finite element programs.