Elasticity deals with elastic stresses and strains, their relationship, and the external forces that cause them. An elastic strain is defined as a strain that disappears instantaneously once the forces that cause it are removed. The theory of elasticity for Hookean solids – in which stress is proportional to strain – is rather complex in its more rigorous treatment. However, it is essential to the understanding of micro- and macromechanical problems. Examples of the former are stress fields around dislocations, incompatibilities of stresses at the interface between grains, and dislocation interactions in work hardening; examples of the latter are the stresses developed in drawing, and rolling wire, and the analysis of specimen–machine interactions in testing for tensile strength. This chapter is structured in such a way as to satisfy the needs of both the undergraduate and the graduate student. A simplified treatment of elasticity is presented, in a manner so as to treat problems in an undergraduate course. Stresses and strains are calculated for a few simplified cases; the tridimensional treatment is kept at a minimum. A graphical method for the solution of two-dimensional stress problems (the Mohr circle) is described. On the other hand, the graduate student needs more powerful tools to handle problems that are somewhat more involved. In most cases, the stress and strain systems in tridimensional bodies can be better treated as tensors, with the indicial notation.