A moment (polar) theory of deformable solids is constructed for anisotropic media such as polarizable piezoelectric ceramics. The linear theory is considered in detail and an explanation of the non-linear change in the electric field inside a polarized piezoelectric material (the Mead effect) is given. The classical theory of electromagnetic effects in solids does not enable certain observed effects to be described (for example, the Mead effect /1/). Attempts to eliminate this drawback of classical theory /2, 3/ rest on the introduction of the polarization gradient into the enthalpy as a parameter of the process. Models of complex media which takes into account the internal mechanical and electromagnetic moments have been constructed in electrodynamics (for example /4, 5/) when electromagnetic fields interact with the medium. Below, a solution of the problem is given and an example of a natural description of the Mead effect is presented.