Non-destructive evaluation of heterogeneous materials is of major interest not only in industrial but also in biomedical fields. A special case is the functionally graded material. This case is particularly interesting in modeling biological media such as the bone tissue, the skin or the arterial wall. A lot of works have been done considering the propagation of elastic waves in a laterally varying plate waveguide. However all the above-mentioned biological media are curved and a more realistic model could be a cylindrical waveguide. In this presentation, an original method is proposed to solve the wave equation in the frequency domain in an anisotropic radially graded tube without using a multilayered model. This method is based on an analytical solution, the matricant, explicitly expressed under the Peano series expansion form. The dispersion curves of the different types of modes (longitudinal, flexural and torsional) propagating in a cylindrical waveguide are calculated. They can be compared to the results - dispersion curves of the "Lamb waves" - obtained with the same method applied to the elastic wave propagation in a plate with laterally varying elastic properties. Then the influence of the curvature could be evaluated and the criteria of relevancy of a plate model investigated. Furthermore, there is a major issue in characterizing cylindrical structures with radially varying properties in order to assess the bone strength evaluation using the phalanx as the anatomical measurement site; in this context, the present study is promising.