<p>In this study, we create a method to examine how sound behaves when it hits a rectangular flexible cavity filled with porous materials and partly covered by elastic membranes. The main aim is to analyze how the coupling between the modes of the porous medium and the elastic structural modes of the cavity affects sound attenuation, leading to the emergence of non-orthogonal propagating poroelastic modes. A mode-matching approach is formulated to characterize the scattering properties of the waveguide, accounting for the interaction between the elastic membrane modes, the inlet/outlet acoustic modes, and the cavity’s porous modes. The formulation leverages the generalized properties of the eigenmodes to ensure computational efficiency and accuracy. Numerical results demonstrate that the poroelastic enclosure substantially enhances acoustic attenuation, strongly influenced by the resonant modes of the flexible boundaries. These findings emphasize the importance of incorporating poroelastic effects in the design of advanced acoustic enclosures and noise-control devices.</p>