It is well known that flow past wall apertures and wall cavities can generate sound. This resulting sound is most often undesirable. For underwater applications, such as flow past cavities in a ship's hull, the constancy of the phenomenon warrants passive control to reduce the acoustic radiation. In this research aperture shape is studied as a passive control mechanism. The Rayleigh conductivity for apertures of different shapes in the presence of one-sided grazing mean flow subject to an externally applied pressure perturbation is investigated numerically. Physically, the external pressure perturbation can result from an external sound source or large scale structural vibration. Because the linear stability of the shear flow over the aperture is governed by the properties of the Rayleigh conductivity, studies of the Rayleigh conductivity as a function of Strouhal number determine the frequency and flow speeds which correspond to self-sustaining oscillations of the flow and acoustic radiation. It is shown that all symmetric apertures with smooth leading edges behave similarly. For example, circular, square, triangular, and cross-shaped apertures all show similar conductivity patterns. However, results show that the conductivity can be altered by making either the aperture asymmetric or the leading edge of the aperture jagged.