This paper presents an acoustic design sensitivity (ADS) analysis on sound radiation of structures by using the boundary element method (BEM). We calculated the velocity distribution of the thin plate by analytical method and the surface sound pressure by Rayleigh integral, and expressed the sound radiation power of the structure in a positive definite quadratic form of the Hermitian with an impedance matrix. The ADS analysis of the plate was thus translated into the analysis of structure dynamic sensitivity and impedance matrix sensitivity. Finally, taking a simple supported thin plate as a simulation example, we investigated the relationships among the sound power, excitation frequency and thickness of the plate. The sound radiation power of the plate has a sharp rise in the vicinity of the plate natural frequency. The method proposed is verified to be able to predict the sound radiation of a thin plate with arbitrary boundary conditions and provide a theoretical basis for structural low noise design which is important to engineering design.