Unsteady compressible flow solutions around a sharp-edged rectangular flat wing of an aspect ratio of 1.0 are obtained using a parallel Reynolds-averaged Navier-Stokes algorithm. The simulated cases are obtained for Mach numbers of 0.42-0.87 and Reynolds numbers of the order of 200 000-300 000 in the transitional flow regime up to an angle of attack of 15 degrees. A Degani-Schiff modification for the Baldwin-Lomax turbulence model is used to distinguish between the boundary layers and the primary and secondary vortices over the flat plate. Unsteady vortex shedding frequencies and Strouhal number variation with the angle of attack are obtained by using the fast Fourier transform. The flow around the low-aspect-ratio rectangular flat wing is strongly dominated by the leading- and side-edge vortices and flow separations. The numerical results are compared with the prior experimental data acquired at the von Karman Institute that shows a mix of laminar/transitional flow. In the simulations, top surface pressures of the rectangular flat wing are well predicted except in the leading-edge region. Time-mean averaged surface flow topologies are also found to be in good agreement with the experiment. Complex flow structures, including the primary and secondary separation bubbles and the footprints of the primary and secondary vortex cores, are well captured through the use of the modified algebraic turbulence model.