Abstract: Up to now, the response analysis and optimization of acoustic metamaterials are mostly based on deterministic parameters and deterministic models.However, in the real engineering world and structure design fields where there are many uncertainties, such as the uncertain of material properties and geometric parameters.If the effects of uncertain variables on analysis and optimization of acoustic metamaterials are not taken into account, the analysis and optimization results may not true.Aiming at this problem and situation, in this paper where the interval model is introduced into multilayer-metamaterials with perforated apertures, and interval Chebyshev expansion-Monte Carlo simulation method (ICE-MCSM) of multilayer-metamaterials with perforated apertures for transmission characteristic is proposed.In ICE-MCSM, truncated Chebyshev polynomials is applied to surrogate the transmittance of multilayer-metamaterials with perforated apertures;therefore, the surrogate model of transmittance is constructed.The samples of interval variables are produced by Monte Carlo method, then the values of these samples are substituted into the surrogate model of transmittance to predict the interval bounds of multilayer-metamaterials with perforated apertures under single-interval variable and multi-interval variables.The results of numerical analysis show that the upper interval bounds and lower interval bounds calculated by ICE-MCSM match the response yields by direct Monte Carlo simulation method (DMCSM).Compared to DMCSM, ICE-MCSM achieves a higher accuracy in interval bound analysis, so ICE-MCSM can effectively and efficiently analyze the interval bounds of multilayer-metamaterials with perforated apertures under uncertain interval variables.Thus, this proposed method in this paper can have promising prospects in real world engineering applications.