In this article, the wave propagation in an infinite piezoelectric solid cylinder of an arbitrary cross section is studied. In the analysis, the boundary conditions are satisfied by the use of Nagaya’s Fourier expansion collocation method. The frequency equations for symmetric and antisymmetric cases are obtained and analyzed numerically for longitudinal and flexural waves for the piezoceramic material PZT‐4. The vibrations of circular and elliptical cylinders are investigated and the results are tabulated. The results obtained for a circular cross section are compared with the available results. The frequency versus the aspect ratio (the ratio of the semimajor and semiminor axes of the elliptical cylinder) is plotted and the dispersion curve is also presented.