This thesis presents computational analysis of sound radiation of plates with arbitrary shapes. A theory of determining the correlation between structure vibration and radiated noise by the finite element method is established. The sound pressure is derived by transforming the bending strain energy of flexural vibration into the strain energy of tension or compression of the bar, which is equal to modal strain energy of bending for the plate element. A fully conforming plate bending element with arbitrary triangular shape is used in the finite element analysis. The element incorporates 18 generalized coordinates, namely the tranverse displacement and its first and second derivatives at each vertex. Computational results are obtained for the plates having shapes of rectangle, equilateral triangle, and right triangle with edges simply supported or clamped. Reasonable results are achieved in all cases of shapes.