The existed drum-like silencer usually consists of expansion chamber with RBC (rigid back cavity) and tensioned membrane. With the effect of vibration radiation of the membrane, the transmitted acoustic energy can be reduced. In order to enable the silencer with ability of vibration isolation, a new type of silencer with FBC (flexible back cavity) was presented. The acoustic theoretical model was established using Fourier-Galerkin method. Then, the TL (transmission loss) characteristic was compared with the RBC model. Further, the silencing mechanism of the FBC silencer was studied, and the influence of the FBC parameters on the performance was also analyzed. Results indicate that the proposed FBC silencer has a better performance in low frequency. Compared with the RBC silencer having the same structural size, it can greatly improve the acoustic absorption band can be improved.