Aiming at the rear disc brake squeal for an SUV, the finite element model (FEM) of contact coupling of disc brake was established by using finite element software. The validity of the FEM is verified by the experimental modal analysis method. The complex modal analysis method was used to analyze the unstable modes of the system under two kinds of friction coefficients. In order to solve the problem of brake squeal, the method of sticking silencing sheet on the brake block backboard was adopted in which the damping of the silencer. In the simulation, the damping of the silencing sheet is described by Rayleigh damping. The simulation results show that the silencing sheet can effectively suppress brake squeal and improve the stability of the system.