AbstractThe motion of an ordinary Newtonian fluid in a channel caused by a pressure gradient alone, or caused by the motion of one of the walls, can be obtained separately; and the problem of generalized Couette flow (the motion due to both causes simultaneously) can be obtained by superposition. For an Ellis fluid, because of the nonlineraity of the viscosity‐stress law, the principle of superposition is not applicable. This paper is devoted to the solution of this problem of generalized Couette flow of an Ellis fluid in parallel flat plate and circular annular channels.