A theory of long wavelength excitations localized at the apex of a semi-infinite wedge of arbitrary interior angle, made up of an anisotropic cubic piezoelectric elastic medium, is presented. The wedge surfaces are assumed to be coated with an infinitesimally thin, grounded conductor. The equations of motion are solved numerically by first mapping the wedge into a right angle wedge, and then expanding the displacement components and the scalar potentials in double series of Laguerre functions.