This paper focuses on the mechanism of sound radiation from vibrating structures in the air field. First, under a simply supported boundary condition, we discuss the characteristics of sound intensity and radiation efficiency for two types of structures (circular plate and rectangular plate). Second, we simplify a two-dimensional rectangular plate as a one-dimensional thin plate. Together with the preceding sound radiation theorem, the mechinical mechanism of sound radiation corresponding to the linear and nonlinear thin plate will be investigated. A analysis of sound pressure and intensity indueced by the vibrating linear and nonlinear thin plate with the simply supported boundary condition will be perfromed, and the influnece of different mode shapes be discussed. Then, induced sound intensities corresponding to distinct ranges in the air field will be also observed. Finally, the comparison of sound pressure will be executed by discussing the relevant factors of the nonlinear thin plate involving the damping, stiffness, and perturbation coefficient.