Open cavity flow is that of most interest to researchers. The flow is typical to that found to exist in the bomb bay of the F-111 and is characterised by intense acoustic levels. A review of the work of previous experimental researchers is included for comparison with the findings of the present thesis. The flow physics indicate that a series of vortices travel downstream in the cavity and are driven by vorticity generated at the upstream lip of the cavity. When strengthened the downstream moving vortex influences the mass addition and expulsion at the trailing edge initiating a pressure wave which propagates upstream and sustains the process of completing the feedback lopp. These features are elucidated upon in the present thesis. The flow at Mach 0.85 and Mach 1.19 is analysed with only differences in the external stream being apparent for the higher Mach number case. The suppression of the acoustic environment is investigated by sloping the aft wall of the cavity. The results of the CFD study are used to examine why sloping of the aft cavity wall is successful. It is shown that the flow tends towards a steady state and the results are compared to the hypothesis of Heller and Bliss. This hypothesis is substantiated by the present simulations and in doing so the work demonstrates the ability of CFD to be used as a tool in conjunction with experimental methods to enhance the understanding of cavity flows. An area of cavity flows for which information is sparse is for the transitional cavity flows. A review of the literature shows that the 4 types of cavity flow exist at supersonic speeds and these are identified by the CFD. The results of the computational study are used to examine when the impingement and exit shocks, characteristic of closed cavity flow, collapse to form a single shock wave. This point is defined as L/Dcrit and occurs when the vertices of the separation and recompression wakes merge. It represents the boundary between transitional-closed flow and closed flow and the CFD predictions are compared to Prandtl-Meyer theory when investigating the position of L/Dcrit.