The reduction of vibration and noise is getting more and more significant in machine design, because it is accepted as a measure of quality. Thin plate structures are normally used for the housing of machines and instruments, and their vibration originates so-called structure-borne noise. From these view points, a method of optimum design of thin-plates for low noise in developed. The finite element vibration analysis and the boundary element acoustic analysis are combined and used to evaluate the sound power radiated from the plate, and it is minimized with respect to the thickness distribution of the plate. The result is compared with the plate of low vibration and the similarity of the methods is discussed.