Abstract: Acoustic metamaterials have been widely used in the field of sound absorption. This paper studies the random response of a monostable acoustic absorber model with noise excitation. Firstly, based on the Ivanov transformation, an approximate equivalent system with non-smooth functions is obtained. Then, the energy envelope random averaging method is used to approximate the stationary response of this equivalent system. With the help of non-smooth inverse transformation, the approximate probability response function of the original system is obtained. In order to verify the correctness of the obtained results, corresponding numerical simulations were carried out on the original system, and the results show the effectiveness of the approximation method. In addition, the effects of system damping and noise amplitude on random response are discussed. Results show that noise can affect the sound absorption efficiency of the sound absorber.