A computational study of laminar/turbulent and subsonic/supersonic horseshoe vortex systems generated by a cylindrical protuberance mounted on a flat plate is presented. Various vortex structures have been predicted and are discussed. For a low subsonic laminar flow, the number of computed vortex arrays increases with Reynolds number (with fixed incoming boundary-layer thickness), in agreement with experimental and previous numerical observations. The relationships among pressure extrema, vorticity, and the singular points in the flow structure on the plane of symmetry over the flat plate are studied. Mach number effects have also been investigated for laminar flow at one Reynolds number. The outermost singular point moves upstream when freestream Mach number increases. The size of the whole vortex structure increases dramatically due to shock-wave/boundary-layer interaction. The computed laminar horseshoe vortex systems start from a saddle point of attachment. In the case of a supersonic turbulent flow at a high Reynolds number, the computed results predict the same features as those indicated by the experimental results, such as the upstream shock-wave/ boundary-layer interaction and the classical horseshoe vortex system starting from a saddle point of separation. The calculations provide details of the downstream wake/shock-wave interaction and the near wake tornadolike vortex structure. The overall flow topology is discussed.