Acoustic radiation from cylindrical shells stiffened by two sets of rings, with constrained layer damping (CLD), is investigated theoretically. The governing equations of motion for the cylindrical shell with CLD are described on the basis of Sanders thin shell theory. Two sets of rings interact with the host cylindrical shell only through the normal line forces. The solutions are derived in the wavenumber domain and the stationary phase method is used to find an analytical expression of the far-field sound pressure. The effects of the viscoelastic material core, constrained layer and multiple loadings on sound pressure are illustrated. The helical wave spectra of sound pressure and the radial displacement clearly show the vibrational and acoustic characteristics of the stiffened cylindrical shell with CLD. It is shown that CLD can effectively suppress the radial vibration and reduce acoustic radiation.