An analysis is presented for wave propagation in infinite homogeneous elastic plates of piezoelectric materials. The analysis is an extension to the work by Shuvalov [1] on wave propagation in general anisotropic elastic plates. A real form of dispersion equation is provided for a piezoelectric plate subjected to different boundary conditions on the plate surfaces. Perturbation theory [2] is exploited to obtain long-wavelength low-frequency approximation for physical quantities of wave propagation, including wave amplitude, stress, electric potential, electric displacement and velocity.