The problem of stationary flow of a nonlinearly viscous fluid is studied under the “velocity‐pressure” mixed formulation, the surface forces are prescribed on one portion of the boundary and the velocities are given on the other portion. The problem is considered under Stokes approximation, i.e., the inertia forces are neglected. Existence and uniqueness are proved, and finite element approximation for velocity and pressure as well as iterative methods are studied.