The four pole concept has been used to analyze gas pulsations in acoustic cavities for a long time. In this study, the four pole parameters for one dimensional (1-D) to three dimensional (3-D) cavities are applied to model a real compressor head with irregular corners and flow obstacles, and a bullet shaped muffler by the idealized rectangular box and circular cylinder approximations. The theoretical results of the transfer functions are calculated from four poles and compared to the experimental data. The comparisons show that certain response frequencies shift between idealized theory and experimental data due to the limitations of an idealized shape analysis for practical applications. In addition, the anechoic termination assumption, which is usually used in compressor discharge modeling, is discussed in this paper. The transfer functions of the above muffler model with different discharge pipe lengths and damping, and horn shaped pipe are simulated and compared. The results represent the typical data measured from experiments.