Acoustic resonances leading to high unsteady pressure levels may occur in flow past cavities. The resonance loop involves a coupling between the downstream-propagating instability wave on the shear layer spanning the open face of the cavity, and acoustic waves propagating within the cavity.The elements of the disturbance field are coupled by the scattering processes that occur at the upstream and downstream ends of the cavity. A theoretical prediction method is developed which combines propagation models in the central region of the cavity with scattering models for the end regions. In the analyses of the scattering problems at the cavity ends, the square-corner geometry is treated exactly, by a method employing the Wiener-Hopf technique. The global analysis provides the frequency and growth (or decay) rate of each mode. The predicted frequencies are in generally good agreement with existing.