Shear flow past a cavity involves a complex fluid dynamic process. Of vital importance is the occurrence of self-sustained oscillations that give rise to tones and the amplitudes of which may be further amplified if the hydrodynamic mode is coupled with the cavity mode. Extensive efforts have been made to investigate the mechanisms of such a simple yet compelling system as well as to predict the noise generated, while most of them are focused on geometry of rectangular shape. For an irregular shaped cavity, numerical methods are usually used which are computationally expensive. A method is developed to predict the tones generated by the shear flow past an open cavity of a complex geometry. In view of the feedback process involved within the system, a describing-function method decomposing the system into a non-linear part and a linear part is used. The linear description function is established by the patch mobility method where the transfer function between patches is extracted from finite element results, while the nonlinear description function is established based on the vortex sound theory. The proposed method showed a superb computation efficiency over CFD method and its accuracy was justified by comparing with the results of public literature.