The free vibration of a disk-beam coupled system having cyclically symmetric structure is investigated by the Ritz method in this study. The orthogonal polynomials generated using the Gram-Schmidt process and the eigenfunction of a uniform disk are employed as admissible functions. The continuity conditions between the disk and beams are satisfied by means of artificial springs at their joints. By this approach, the mass matrices derived from kinetic energies of the system become diagonal, and this will make the numerical manipulation of the matrices easy and stable. It is also described in this paper that the mode shapes of the disk-beam coupled vibration consist of specific circumferential wave components and thus the modes can be classified. Numerical calculations are carried out, and the frequency parameters and mode shapes are obtained to investigate the vibration of the disk-beam coupled system.