For a semi-infinite piezoelectric body with uniform or variable cross section we establish the exponential decay of the internal energy relative to the portion of the body beyond a distance x3 from the base:​ Saint-Venant's principle. All possible combinations of physically admissible boundary conditions are examined. The stabilizing effect of the electric field on the decay length is shown. Finally the total internal energy is estimated in terms of the data, making use also of the Korn inequality.