In order to evaluate the acoustic-radiation performance of two functional materials, the vibro-acoustic radiation of a typical cylindrical shell with stiffened ring ribs is calculated based on FEM and BEM method, and the results agree well with the experimental results. According to the equivalent principle of temperature and frequency, the dynamic mechanical parameters of viscoelastic core material for acoustic absorption were acquired from the results of dynamic thermodynamic experiments. The coupling effect of water and the shell was simulated by finite element method. Finally, the acoustic radiation field of sandwich-shells with different core materials excited by a point source was calculated by means of indirect boundary method. The results show that the circumferential mode has an important influence on the modal damping ratio of both the sandwich shell with buoyancy core and sandwich shell with sound-absorption core, whilst axial mode just has a significant effect on the modal damping ratio of the sandwich shell with sound-absorption core. The peak value of the acoustic power of the sandwich shell with buoyancy core and sandwich shell with sound-absorption core is 21.38 dB and 56.55 dB lower than that of the steel shell respectively. When the combination of the above two functional materials in different proportion were used as the core material, the radiation acoustic power decreases with the increasing proportion of the sound-absorption material, but the decrease amount diminishes gradually.