Machinery and appliances are usually enclosed by a panel structure, one of whose functions is to reduce the sound power radiated by the equipment. The theory employed in building acoustics for sound transmission through walls and partitions is not generally adequate for these situations since the sound field inside the enclosure is rarely diffuse, owing to the geometry of the machinery or appliance with respect to the enclosing surfaces. This paper outlines a theoretical approach that does not assume a diffuse sound field within the enclosure. Rather, it models the close dynamical coupling between the enclosure panels and the vibrating machinery inside. Also recognized is that the sound power radiated by the machine is affected by the enclosure, a fact that can be generally ignored in building acoustics. The theory shows the effect on acoustical performance of structural damping of the panels, acoustical absorption inside the enclosure, and the space between the machinery and the enclosure.