Regarding the vib-acoustic performance of internal coupled structures, basically all relevant studies have been confined to the classic form of connections. In this investigation, the boundary and internal elastic constraint matrices of the coupled structure are established, the vibration and sound calculation model of the coupled structure is then established, and numerical analysis is performed to show the effect of constraint stiffness on the vibration and acoustical performance of a coupled plate-cylindrical shell system. The results show that impedance matching between the structures is improved with the increase of the elastic connection stiffness, which is conducive to the vibration energy propagation. Moreover, the supporting coupling stiffness between elastic coupled structures plays an important role in vibration energy transfers.