The effects of shear deformation and piezoelectric-elastic coupling are considered. The beam is divided into different regions in order to describe the different sizes and positions of the delamination easily. The governing equations for the flexural wave propagation in the beam are derived based on Timoshenko beam theory. According to the potential distributing simplification for the long wave propagation, the harmonic response of the cantilever beams without the additional potential is gained. The dispersion relations and the closed solution of the displacements and the potentials are obtained. The influence of delamination parameters on displacements and potentials is discussed.