The first attempt to deduce the general equation of equilibrium and vibration of elastic solids was made by Navier (1785-1836) in a remarkable memoir read on May 14, 1821, see Sokolnikoff (1946). This date marks the birth of the mathematical theory of elasticity. Starting with the picture of mathematical interactions in which the force acts along the line joining two particles and are proportional to the change in distance between them, Navier deduced set of three macroscopic differential equations for the components of displacements in the interior of an isotropic elastic solid. Navier’s work attracted the attention of Cauchy (1789-1857), whose proceeding from different assumption gave a formulation of linear theory of elasticity. Instead of starting with some specific law of molecular interactions, Cauchy showed that state of stress at an interior point of deformable body is completely determined by a set of nine functions. When the body is in equilibrium, these nine functions reduce to six because of some symmetry relations. The mathematical theory of elasticity which is widely accepted has been derived by Cauchy (1823).