This book presents computational procedures for the stress integration of inelastic constitutive relations within the incremental-iterative finite element analysis and general strain-driven problems of solids and structures. The book gives the physical and theoretical foundations of inelastic material models commonly used in engineering practice, and focuses on the formulation of robust, efficient and accurate computational algorithms for the response solution of 2-D and 3-D solids, shells, and beam and pipe structures. The algorithms are based on the concept that the implicit stress integration can frequently be reduced to the solution of a single nonlinear equation (an equation for a governing parameter). Many solved engineering examples illustrate the effectiveness of the computational procedures and elucidate inelastic material behavior. The computational schemes can be used for further developments of stress integration algorithms in topics of inelastic material modeling not included in the book.