In a recent paper by Berg et al. [Berg, M., Hagedorn, P., Gutschmidt, S., 2004. On the dynamics of piezoelectric cylindrical shell, Journal of Sound and Vibration 274, 91–109], equations for the piezo-ceramic cylindrical shell are derived. These equations differ from known equations because the electric field is not assumed to be constant over the thickness, but is obtained by solving the Maxwell’s equation. The considered shell model is the so-called Flugge’s shell theory where the transverse shear deformations is not considered, and the Maxwell’s equation is reduced in form. In this paper the analysis of wave propagation in Reissner–Mindlin piezoelectric coupled cylinder is studied. The shear strain is modelled and the Maxwell’s equation is fully considered.