In solid mechanics, the linear stability analysis of an elastic solution is studied using the method of incremental deformations superposed on finite deformations. The method of incremental deformation can be used to solve static, quasi-static and time-dependent problems. The governing equations of the motion are ones of the classical mechanics, such as the conservation of mass and the balance of linear and angular momentum, which provide the equilibrium configuration of the material. The main corresponding mathematical framework is described in the main Raymond Ogden's book Non-linear elastic deformations and in Biot's book Mechanics of incremental deformations, which is a collection of his main papers.