ThisElasticity chapterLinear elasticity provides a mathematical formulation for the deformationDeformation of elastic bodies considered as continua under isothermal conditions. We first introduce basic concepts in the theory of elasticityElasticity and derives a system of fundamental equations based on conservation laws for various physical quantities. Specifically, we consider conservation laws for momentum, angular momentum, mass, and energy. These laws lead to the equations of motionEquations of motion, symmetry of the stressTensor tensorStress tensor and constitutive equationsConstitutive equations for elastic materials. The formulation thus obtained is applied to some computational examples, and finally, some concepts useful in considering earthquake rupture phenomena are introduced. This chapter is fundamental to the analysis in the following chapters.