Abstract: To obtain a better understanding of compressible vortex dynamics, a numerical investigation of laminar, compressible vortices was conducted using the quasi-cylindrical approximation. The goal was to determine if the phenomena of vortex breakdown would occur. Vortex breakdown is an important and unsolved problem in the field of fluid dynamics. The results show that two possible flow regimes can occur for a potential vortex with a constant edge axial velocity. The first is a vortex that decays in a manner similar to the incompressible vortices examined by Batchelor. The centerline axial velocity decay is driven by the edge axial velocity. Far downstream, the axial velocity profile is nearly constant with the tangential and radial velocities approaching zero. The second flow regime occurs when the edge axial velocity is sufficiently small and vortex breakdown occurs. For a given Mach number, the critical value of edge axial velocity for breakdown was determined. For a set value of the edge axial velocity, the stream wise distance to obtain vortex breakdown was a strong function of the Mach number. As the Mach number increased, the distance to vortex breakdown was decreased.