This work explores the effect of the electric field gradient in the constitutive behavior of elastic dielectrics by analyzing the anti-plane surface waves propagating over a half-space of polarized ceramics. The obtained frequency equation shows that the gradienteffect makes the surface waves dispersive, although they are known to be non-dispersive according to the classical theory of linear piezoelectricity that neglects the gradienteffect. This analysis further shows that there exists a microstructural characteristic length, comparing to which the dispersion is significant for short waves while negligible for long waves. This suggests that the dispersion may have significante ects for very small surface acoustic wave devices operating with high-frequency short waves.