Although S. N. Curle's very useful formula for aerodynamic sound radiated from a rigid surface can be applied to closed fluid circuits by the method of images, this procedure is not practical for cavities of complex shape. Sound fields in such cavities are best described with standing waves. However, substitution of an orthonormal mode expansion into the inhomogeneous wave equation results in volume integrals of dilatation source terms for the generalized model loads [N. A. Cumptsy and D. S. Whitehead, J. Sound Vib.18, 353–369 (1971)]. Since the dilatation field is usually not known, the formal solution is difficult to apply. This paper presents an expansion of the sound field in a cavity in terms of nonorthogonal functions which results in a coupled set of equations with the generalized loads in terms of surface pressures (as in Curle's derivation), plus quadrupole terms. When the equations can be conveniently uncoupled and the quadrupole terms neglected, this formalism is very useful. Some of the cavity and flow geometries for which these two simplifications can be made and discussed.