Acoustic scattering from the submerged finite periodically ribbed two concentric cylindrical shells, insonified by an incident plane wave, is studied. Motion of the shell is described by Donnell equations, while the motion of the disks is described by thin plate motion equations and plane ströss equations ignoring the effects of axial forces on the disks. Through angle-frequency spectra, besides the elastic waves of the shells, the contributions of the fluid between the inner and outer shells and the interaction of the inner and outer shells with the disks play an important role in the far scattering field. There are fine echo waves such as Bragg scattering and fluid-added waves excited on the angle-frequency spectra. Finally the theories are verified by experiments.