A computational method is presented for assessing the sound power characteristics of machines. The method, which is based upon a Helmholtz integral formulation, requires a knowledge of the geometry and the modal characteristics of a machine’s vibrating surfaces so that the pressure on the surface can be computed. Closed form integration of the associated surface integrals is carried out in a piecewise manner over planar surface elements in the shape of rectangles or triangles. This choice of element allows the grid geometries associated with the acoustic power computations to be made identical to those used in existing structural modal analysis methods. In this way, the sound power characteristics of a given machine can be computed in terms of the sound power radiated by each of the structural modes comprising the overall response. The structural modes can then be ranked in order of their radiation efficiency for purposes of noise control treatments. The accuracy of the method is demonstrated by calculating the pressure on the surface of a uniformly pulsating sphere and of an oscillating sphere for values of ka (dimensionless frequency) up to 10.