In this chapter, the general problem of the non-homogeneous and anisotropic threedimensional linear elastic body is formulated. The properties of linearity, homogeneity and isotropy concern exclusively the constitutive relations which link stresses and strains; they in any way affect neither the kinematic relations, which define dilations and shearing strains, nor the static relations provided by the indefinite equations of equilibrium. An intimate correlation exists between the static and kinematic relations, in that the two corresponding matrix operators are each the transpose of the other. The same correlation is present, at a finite level, in the case of rigid body systems, as has been seen in Chapter 3.