This book describes the theoretical foundations of inelasticity, its numerical formulation and implementation. The subject matter described herein constitutes a representative sample of state-of-the-art methodology currently used in inelastic calculations. Computational Inelasticity will be of great interest to researchers and graduate students in various branches of engineering, especially civil, aeronautical and mechanical, and applied mathematics. 1. Motivation. One-Dimensional Plasticity and Viscoplasticity -- 2. Classical Rate-Independent Plasticity and Viscoplasticity -- 3. Integration Algorithms for Plasticity and Viscoplasticity -- 4. Discrete Variational Formulation and Finite-Element Implementation -- 5. Nonsmooth Multisurface Plasticity and Viscoplasticity -- 6. Numerical Analysis of General Return Mapping Algorithms -- 7. Nonlinear Continuum Mechanics and Phenomenological Plasticity Models -- 8. Objective Integration Algorithms for Rate Formulations of Elastoplasticity -- 9. Phenomenological Plasticity Models Based on the Notion of an Intermediate Stress-Free Configuration -- 10. Viscoelasticity.