An analysis is conducted of the two-dimensional flow of Bingham solids between two rotating plates. The maximum friction law is adopted at the plate surface. An asymptotic analysis of the solution is performed in the vicinity of the friction surface. Its results are used in a numerical procedure to obtain an accurate approximation of the solution near the friction surface. The through thickness distribution of velocities, the equivalent strain rate, and stresses is illustrated. Qualitative features of the solution are emphasized. The results are compared with the solution for rate-independent materials.