Most materials have an ability to resist and recover from deformations produced by forces. This ability is called elasticity. It is the foundation for all aspects of rock mechanics. The simplest type of response is one where there is a linear relation between the external forces and the corresponding deformations. When changes in the forces are sufficiently small, the response is (nearly) always linear. Thus the theory of linear elasticity is fundamental for all discussions on elasticity.

The theory of elasticity rests on the two concepts stress and strain. These are defined in Sections 1.1 and 1.2. The linear equations relating stresses and strains are discussed in Section 1.3 for isotropic materials, and in Section 1.7 for anisotropic materials. Linear thermoelasticity is discussed in Section 1.5.

The region of validity for linear elasticity is often exceeded in practical situations. Some general features of nonlinear behaviour of rocks are described in Section 1.8.

In petroleum related rock mechanics, much of the interest is furthermore focused on rocks with a significant porosity as well as permeability. The elastic theory for solid materials is not able to fully describe the behaviour of such materials, and the concept of poroelasticity has therefore to be taken into account. The elastic response of a rock material may also be time dependent, so that the deformation of the material changes with time, even when the external conditions are constant. The elastic properties of porous materials and time-dependent effects are described in Sections 1.6 and 1.9, respectively.