Structure-borne refrigeration compressor noise reduction has been a major concern for the industry. Structural modifications for noise reduction have often been carried out on the basis of a vibration or modal analysis of the compressor shell alone. Since there are two dense fluids inside a compressor shell, refrigerant and lubricating oil, significant dynamic interaction between the shell and the fluids is likely to occur. The major focus of this paper is to examine the transmission loss of such shells, considering the fluid-structure coupling. A semi-analytical finite element method is used to find the vibration response of the shell-fluid coupled system when excited by acoustic pulsations in the shell cavity caused by the reciprocating mechanism of the compressor. To calculate the acoustic and structural response, a special modal superposition technique based on adjoint eigenvectors is used since the finite element formulation leads to unsymmetric matrices. Once the structural vibration response has been computed, an axisymmetric boundary integral technique is used to predict acoustic pressures on the outside surface of the compressor shell. The transmission loss is then computed by comparing the acoustic pressures inside the cavity with the pressures on the outside surface. It is demonstrated that transmission loss is high for the first few modes of the shell and decreases with increase in the circumferential mode number. For a given circumferential mode the transmission loss is shown to increase with increase in axial mode number.