Abstract We examine certain analytic and numerical aspects of optimal control problems for a Ladyzhenskaya model for stationary, incompressible, viscous flows. The control considered is of the distributed type; the functionals minimized are the L 2- distance of candidate flow to some desired flow and the viscous drag on bounding surfaces. We show the existence of optimal solutions and justify the use of Lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced. We study the regularity of solutions of this system. Then, we consider approximations, by finite element methods, of solutions of the optimality system and examine their convergence properties.