In this study, a Green's function-based semi-analytical method is presented to predict the transmission loss (TL) of a circular chamber having concentric perforated screens. Initially, the Green's function is developed for a single-screen configuration as the summation of eigenfunctions of the inner pipe in the absence of the mean flow. The inlet and the outlet ports are modeled as oscillating piston sources. A transfer matrix is formulated from the velocity potential generated by the piston sources. The results obtained from the proposed method are validated with the numerical and analytical models and with the experimental results available in the literature. Later, the method has been extended to the double-screen configuration. The effect of the additional perforated screen on the TL is studied in terms of the surface impedance of the chamber. Along with grazing flow considerations, guidelines are provided to incorporate more concentric perforated screens into the formulation. © 2020 by ASME.