In Chapter 4, the linear relations of the local gradient theory of dielectrics are tested on some simple problems. In particular, they are used to study the effect of a free surface on the stress–strain state and polarization of elastic bodies having plane and cylindrical surfaces, as well as of a thermoelastic hollow sphere. Using the relations of the local gradient theory of elasticity, which involves the irreversibility of the local mass displacement, the formation of a near-surface inhomogeneity of the fields in an isotropic infinite layer is investigated. A relation for the surface energy of deformation and polarization for non-ferromagnetic polarized solid bodies is obtained.