Acoustic metamaterials (AMs) are man-made composite materials. However, the random uncertainties are unavoidable in the application of AMs due to manufacturing and material errors which lead to the variance of the physical responses of AMs. In this paper, an uncertainty model based on the change of variable perturbation stochastic finite element method (CVPS-FEM) is formulated to predict the probability density functions of physical responses of AMs with random parameters. Three types of physical responses including the band structure, mode shapes and frequency response function of AMs are studied in the uncertainty model, which is of great interest in the design of AMs. In this computation, the physical responses of stochastic AMs are expressed as linear functions of the pre-defined random parameters by using the first-order Taylor series expansion and perturbation technique. Then, based on the linear function relationships of parameters and responses, the probability density functions of the responses can be calculated by the change-of-variable technique. Three numerical examples are employed to demonstrate the effectiveness of the CVPS-FEM for stochastic AMs, and the results are validated by Monte Carlo method successfully.