We now study stress–strain relations, called constitutive equations, as these depend on the constitution (microstructure) of the material. We restrict to time-independent, i.e., elastic-plastic constitutive equations. The experimental observations of elastic-plastic stress–strain relation and fatigue test are described and related material parameters are defined. Simple models of elastic-plastic behaviour for uniaxial tension are developed. The generalised Hooke’s law and its simplifications for various symmetries are discussed. The conditions for superposition of solutions are listed, and Saint Venant’s principle is described. The solution of a cylindrical rod under tension is obtained. Mises and Tresca yield criterion for ductile materials and modified Mohr’s fracture criterion for brittle materials are presented.