The target energy transfer (TET) between a membrane nonlinear energy sink (NES) and the acoustic medium inside a rectangular cavity is studied. The acoustic medium is interacted with a plate and multi-order modes coupling of the 2 structure is considered. Based on the modal expansion approach, with Green’s function, Helmholtz equation and the boundary conditions of the acoustic medium and the plate, the coupling coefficient matrix of the mode of 2 structures is derived. The equations of the membrane NES, multi-order modes of the acoustic medium and multi-order modes of the plate are established, and numerical analysis is used to investigate the TET phenomenon. The results show that in condition of a single-point excitation to the plate, under a certain range of excitation levels, the membrane can be seen as a kind of NES, and the energy in the acoustic medium can be unidirectionally transmitted to the membrane NES and attenuated, reducing the sound pressure level in the cavity. At the same time, it is found that the NES can suppress multi-order sound pressure of the acoustic medium at the same time, and realize the control of cascaded resonance noise.