Exact solution of axisymmetric wave propagation problem in radially and functionally graded circular cylinder made from combination of isotropic and transversely isotropic materials is obtained. This solution is based on exact relationships derived by C. Chree and exact continuity and boundary conditions formulated for the problem with arbitrary number of concentric circular layers. The solutions are obtained for dilatational and shear waves. Frequency spectra of travelling and evanescent waves are plotted for dilatational modes of vibration of two- and three-layered cylinders. Phase velocities are calculated and plotted for the travelling dilatational waves. Peculiarities of wave propagation in the functionally graded cylinders are discussed.