Acoustic surface waves propagating around a piezoelectric cylinder with metallic overlays are investigated. The piezoelectric core is assumed to possess the hexagonal symmetry, and the layer is electrically shorted. The dispersion equation is derived. Numerical results for the phase velocities, the displacement, and potential profiles are presented for different layer materials with various thicknesses. It is found that the thickness of the gold and chromium has a substantial effect on the dispersion, while in the case of aluminum layers little influence is observed. An asymptotic expansion for the dispersion equation is also derived and is found to yield results in good agreement with the exact solution.