The mathematical modelling of the two dimensional compressible for over an open rectangular cavity is considered. The flow field is divided into three regions: (1) the two-dimensional compressible flow outside the cavity which is governed by a convective wave equation; (2) the two dimensional flow inside the cavity for which the mean flow is neglected and thus is governed by the wave equation; and (3) the shear layer spanning the cavity which is the major focus of the investigation. the work of Tam and Block is followed and a method for determining the discrete frequencies of shear layer oscillation is determined including shear layer thickness effects and assuming that the shear layer grows downstream. a line source placed at the trailing edge is used to model the trailing edge interaction process and the analysis of a shear layer excited by a reflected wave of arbitrary frequency is considered. Since the mean flow in the shear layer is nonuniform, standard stability procedures do not work. The nonparallel effects are assumed to be weak. The method of multiple scales is used to analyze the nonparallel stability of the shear layer. The stability characteristics of the shear layer are used in an equation developed by Tam and Block to predict discrete oscillation frequencies. The numerical methods for solving the equations are discussed. Originator-supplied keywords include: Open cavity flows; Nonparallel stability; and Multiple scales.