<p>Membrane-type acoustic metamaterials excel in narrowband sound insulation but suffer from limited broadband efficiency, complex fabrication, poor reliability, and vulnerability to damage. This paper proposes a flexible acoustic metamaterial structure that combines the sound-insulation capabilities of solid materials and membrane-type metamaterials, offering advantages such as flexibility and low weight. The acoustic membrane comprises thin foils of prescribed geometry coupled to enclosed air cavities. Its acoustic impedance is first formulated via the Lagrangian energy principle, from which an analytical expression for sound transmission loss (STL) is derived. Numerical results reveal that the structure supports multiple resonant modes, producing successive STL peaks and yielding a broadband sound-insulation enhancement with an average STL of 30&#xa0;dB. Parametric studies are subsequently conducted to quantify the influence of four key geometric parameters on the membrane’s acoustic performance, leading to an optimized design that balances acoustic efficacy with practical applicability. To validate the theoretical model, three kinds of acoustic membrane samples were fabricated and tested in a semi-anechoic chamber. The experimental STL results showed good agreement with the numerical simulation results based on the finite element method (FEM). This acoustic membrane delivers noise reduction comparable to that of conventional insulation, with particularly pronounced efficacy in the low-to-mid-frequency range (600–4000&#xa0;Hz), which encompasses the dominant noise components of compressors, motors, and household appliances, while offering substantial advantages in terms of mass and cost. With simple fabrication, low cost, lightweight construction, and good flexibility, it holds promise as a substitute for traditional sound-insulation cotton and has potential applications in noise control for industrial sources such as compressors, motors, and engines.</p>