Within the theory of small deformations superposed on a finite one, a consistent linearization for the nonlinear equations of the mechanics of an originally isotropic elastic body in a neighborhood of some initial stress state is carried out in the Lagrange coordinate system. As the elastic potential for the originally isotropic body, we use the representation of the specific strain energy through the algebraic invariants of the Green-Lagrange strain tensor. The linearized constitutive relations and the equations of motion of the prestressed medium are derived that allow taking into account the nonlinear effects of the initial deformation on the elastic properties of the originally isotropic body.