A general procedure for the analysis of curved or flat, thin two dimensional gas cavities such as thin compressor or engine manifolds or so-called thin shell type muffler elements, which can efficiently utilize the limited space of hermetically sealed compressors or small engine compartments, has been developed by the authors (1996a and 1996b), as long as the thickness of the cavities is substantially small compared to the shortest wavelength of interest. However, for an acoustic system which consists of two different thin gas cavities sharing a common line like boundary, some modifications of this general procedure are required. In this study, a simplified refrigeration compressor manifold model, whose geometry is similar to a circular disk box attached to a cylindrical cavity, is investigated. In order to use the general formulations to solve for the forced responses, the natural frequencies and natural modes of this compressor model have to be first determined by a line impedance method proposed by the authors (1996c). Line impedances are formulated, in analogy to line receptances in structural analysis, from the pressure responses of the cylinder and disk cavities to the line volume flow rate inputs which are distributed harmonically along the circular interface of the two subsystems. The frequency characteristic equation is derived and then solved for the natural frequencies and mode shapes of the compressor model. The acoustic four poles and transfer function are finally obtained by substituting the natural frequencies and mode shapes into the general formulations.