The interior of an open cavity exposed to a grazing flow is known to experience strong periodic pressure oscillations sustained for a wide range of flow velocities. In this study, an analytical model was investigated to allow predictions of the amplitude and the frequency of the pressure fluctuations induced inside the cavity. The flow-excited cavity system was assumed to be described in the frequency domain by two gain functions, forming a limit cycling closed-loop. The forward gain function is associated with the excitation mechanism, governed by the shedding of discrete vortices within the shear layer over the orifice. The backward gain function is associated with the acoustic response of the cavity resonator. An original approach was followed to determine the forward gain function, based on the vorticity formulation of the equations of motion (the so-called “vortex sound” theory). The analytical model was experimentally verified for a range of flow velocities and orifice dimensions. The predictions were found to be in good agreement with experimental observation.