The objective of this study is to simulate unsteady, supersonic flow past an open rectangular cavity to better understand the flow physics of the cavity flow oscillations. The simulations are performed for the flow at a free stream Mach number of 1.5. The compressible time-dependent Reynolds-Averaged Navier-Stokes equations in both two and three dimensions are solved using the GASPex software employing the k - ω turbulence model and Roe scheme for the numerical fluxes. The results of the computations are compared with the experimental results in terms of overall acoustic sound pressure levels within the cavity. The results of two dimensional and three dimensional computations are compared to each other as well as the experimental results. Differences between two and three dimensional computations are observed in terms of pressure distribution at several points in the cavity. The amplitude and frequency of the fluctuations are also different. Three dimensional results are closer to the experimental results in literature as expected. The effect of the initial condition on two dimensional simulation results is also examined.