Efforts to control machinery noise at the source have been made for many years. It is well known that machine component vibrations are one major source of noise. In general, a machine will be composed of several components each with its own vibration and sound radiating characteristics. In order to control the noise at the source, a detailed understanding of the noise source is essential. Experimental approaches to attack this problem have been studied extensively. In the current work, however, an acoustic surface intensity function is calculated analytically using boundary element method. The surface intensity value is the time averaged acoustic energy flux radiated from structure surface into the medium. The advantage of using the surface intensity is that it provides the most direct information of energy source strengths on the radiator's surface. The surface intensity values can be displayed on the structure surface which will not only give an overall view of sound radiation associated with the structure geometry but also provide local detail in any zone. Several case studies have been performed which are (1) a finite monopole, dipole and guadrupole, (2) a spinning finite thickness circular disk. Based on these examples, the computed and theoretical results compare very closely.