Flexural wave dispersion in a bi-material solid and hollow circular cylinders is investigated with the use of the three-dimensional linear theory of elastodynamics. It is assumed that on the interface surface of the cylinders the complete contact conditions satisfy. The analytical solution of the corresponding field equations is presented and, using these solutions, the dispersion equations for the cases under consideration are obtained. The dispersion equations are solved numerically and based on these solutions, dispersion curves are constructed for the concrete selected pairs of materials such as Tungsten (inner cylinder material) + Aluminum (outer cylinder material) and Steel (inner cylinder material) + Aluminum (outer cylinder material). The numerical results are obtained for the first and second lowest modes. According to these numerical results the influence of the problem parameters, such as the thicknesses of the external and inner cylinders and the materials of the inner cylinder material, on the character of the dispersion curves is analyzed.