Although compressible swirling flows are often encountered in many diverse engineering applications, the related flow physics is seldom known. Thus, almost all of fluid machinery with the swirling flow are so far designed neglecting the compressibility effects that can lead to mal-operation or performance deterioration of the device. In the present study, theoretical and computational analyses have been carried out to investigate the planar, isentropic, axisymmetric compressible swirling flow. A series of governing equations have derived to disclose the compressibility effects in the swirling flow. The present theoretical results show the choking phenomena which are discussed in terms with the swirl angle and pressure ratio. A computational work has been performed to reveal the complicated flow involved in the compressible swirl flow. It is expected that the present results would be very helpful in designing the flow devices operated at high pressure ratios.