Duct with a flexible plate mounted in its sidewall is sought as an effective means for duct noise control in low frequency range. Most of the existing studies are focused on the transmission loss behavior, while there is little effort devoted to its physical mechanism in terms of energy transmission. Motived by current limitation, a novel and efficient structural-acoustic coupling model is established for the study of vibro-acoustic coupling and energy transmission in a cavity-backed plate duct silencer. Acoustic intensity vector and its divergence are studied to illustrate the structural-acoustic coupling characteristics and reveal the distributions of energy sources and energy sinks. The influence of elastic edge restraints on the sound attenuation characteristics of coupled duct-plate silencer is then addressed and investigated in detail. It is believed that this work will be of great help for engineer to obtain a better understanding on the physical mechanism of such structural-acoustic silencer and achieve the optimal design.