In this work, we are concerned with the finite element approximation for the stationary power law
Stokes equations driven by nonlinear slip boundary conditions of ‘friction type’. After the formulation of the
problem as mixed variational inequality of second kind, it is shown by application of a variant of Babuska–
Brezzi’s theory for mixed problems that convergence of the finite element approximation is achieved
with classical assumptions on the regularity of the weak solution. Next, solution algorithm for the mixed
varia-tional problem is presented and analyzed in details. Finally, numerical simulations that validate the
theoret-ical findings are exhibited.