Purpose <p>Membrane-type acoustic metamaterial is an artificially designed “sub-wavelength” scale material with negative equivalent mass characteristics. It can be combined with vehicle sound absorbing and insulating materials to achieve designable sound insulation properties, especially for mid and low frequency range where better insulation performance, heavier weight of materials. This paper establishes a theoretical analytical model that can be used to analyze the sound insulation properties of membrane-type acoustic metamaterials under general elastic constraint boundary conditions. </p> Methods <p>Uniformly distributed boundary springs are used to simulate general constraint boundary conditions, and the forced vibration equation of acoustic metamaterials under external force excitation is derived based on the Rayleigh-Ritz method (using Gaussian basis functions) and Hamilton’s principle. Combined with the plane wave equation, an analytical model of sound insulation of acoustic metamaterials under general elastic constraints is established. Then three methods, namely theoretical model, Finite Element Analysis (FEA) and impedance tube test, are used to study the sound insulation characteristics of acoustic metamaterials under fixed, simple support and free boundary conditions.</p> Results <p>The results show that the theoretical method is validated by the FEA method and experimental method and the established analytical model is no longer limited to a single boundary condition for analyzing the sound insulation properties of membrane-type acoustic metamaterials, but has strong adaptability to different boundary conditions.</p> Conclusion <p>The results proposed in this paper provides technical supports for complex boundary conditions when membrane-type acoustic metamaterials are applied into vehicle sound absorbing and insulating materials.</p>