Unlike elastic materials, some materials, such as steels or aluminum alloys, exhibit permanent deformation when a force exceeding a specific limit (the elastic limit) is applied and then removed. This behavior of materials is called plasticity, which is the primary topic in Chap. 4. When the total strain is small (infinitesimal deformation), it is possible to assume that the total strain can be additively decomposed into elastic and plastic strains. Sections 4.2 and 4.3 are based on infinitesimal elastoplasticity. In a large structure, even if the strain is small, it may undergo a large rigid-body motion due to accumulated deformation. In such a case, it is possible to modify infinitesimal elastoplasticity to accommodate stress calculation with the effect of rigid-body motion. Since the rate of Cauchy stress is not independent of rigid-body motion, different types of rates, called objective stress rates, are used in the constitutive relation, which is discussed in Sect. 4.4. When deformation is large, the assumption of additive decomposition of elastic and plastic strains is no longer valid. A hyperelasticity-based elastoplasticity is discussed in Sect. 4.5, in which the deformation gradient is multiplicatively decomposed into elastic and plastic parts, and the stress-strain relation is given in the principal directions. This model can represent both geometric and material nonlinearities during large elastoplastic deformation. Section 4.6 is supplementary to Sect. 4.5, as it derives several expressions used in Sect. 4.5. Section 4.7 shows MATLAB codes for elastoplastic analysis. Section 4.8 summarizes the usage of commercial finite element analysis programs to solve elastoplastic problems.