Coupled extensional and flexural cylindrical vibrations of a corrugated cylindrical piezoelectric shell consisting of multiple pieces of circular cylindrical surfaces smoothly connected along their generatrix are studied. To validate the results for the case of relatively thick shells or equivalently high-frequency modes with short wavelengths, existing analysis is extended by considering shear deformation and rotatory inertia. An analytical solution is obtained. Based on the solution, resonant frequencies and mode shapes are calculated.