A two-stage numerical model is developed to understand the energy transmission characteristics through a finite double-leaf structure placed in an infinite baffle subjected to an external excitation and subsequently the sound radiation behavior of the same into the semi-infinite receiving side. In the first stage, a mobility based coupled finite element - boundary element (FE-BE) technique is implemented to model the energy transmission from the primary panel to the secondary panel through an air-gap. In the second stage, a separate BE based model is developed to estimate the sound power radiated by the radiating (secondary) panel into the receiving side which is assumed to be semi - infinite. The advantage of the proposed approach is that it is sufficient to mesh the structural panels alone, thereby reducing the problem dimensions and the difficulty in modeling. Moreover, the developed model can be easily implemented for structures made up of various constituent materials (isotropic or laminated composites) with complex boundary conditions and varying panel geometries. Numerical experiments are carried out for different material models by varying air-gap thicknesses and also by introducing alternate energy transmission path in terms of mechanical links and the obtained results are discussed.