This paper presents a geometric method of solving rotational flow fields. As a prior condition for this method to be applicable, streamlines must be known along the two boundaries of the flow region in question. This method is an extension of a geometric method aE solving potential flows developed by F.O. Ringleb. The method is based on the piecewise approximation of streamlines and their orthogonal trajectories by circular arcs. For both potential and rotational flows, only two-dimensional and axisymmetric flows may be solved, but the fluid may be compressible or incompressible. Examples are worked where curved shock waves have induced rotational flow. Both axisymmetric and two-dimensional flows are treated in the examples.