<p>This paper presents an analytical study of acoustic wave propagation and scattering in a multilayered cylindrical waveguide composed of flexible shell segments joined through flanged interfaces. Such configurations arise in practical applications, including aerospace ducts, silencer chambers, and engineering designs with compliant walls connected via flanged junctions. The acoustic field inside the waveguide is governed by the Helmholtz equation, while the vibration response of the flexible shell is described using the Donnell–Mushtari shell equations. A mode-matching method, incorporating a generalized orthogonality framework for non-orthogonal eigenfunctions, is employed to enforce continuity of pressure and displacement at the interfaces. The formulation is validated through reconstruction of field continuity at the junctions and verification of energy conservation. The truncated solution is then used to investigate the influence of frequency and geometric parameters, such as flange size, shell radius, and chamber length, on transmission and reflection characteristics. Results indicate that attenuation performance can be optimized through appropriate parameter selection, with flange disc size playing a particularly significant role. The proposed framework provides a robust analytical tool for the design and optimization of flexible waveguide systems featuring structural discontinuities and flanged connections.</p>