In the present study, the hoposcotch method was tested for solving the axisymmetric, inviscid, compressible, shock-free flows. The physical space was transformed into a rectangular computational space. Hoposcotch method was applied to solve the unsteady, cylindrical, conserved governing equations of motion in the transformed computational space, with the steady state solution computed as the asymptote of the transient solution. The source flow and the transonic flow through a converging-diverging nozzle were considered as test problems. The solutions were compared with the available
exact, experimental, and numerical results. The method was found to be stable and in excellent agreement with the available results. An advantage of the method is that it is superior in speed (computing time); being 1.8 times faster than MacCormack's method and 2.9 to 7.3 times faster than the reference plane characteristics method.