We introduce a MAC-like scheme (a covolume method on rectangular grids) for approximating the generalized Stokes problem on an axiparallel domain. Two staggered grids are used in the derivation of the discretization. The velocity is approximated by conforming bilinears over rectangular elements, and the pressure by piecewise constants over macro-rectangular elements. The error in the velocity in the H1 norm and the pressure in the L2 norm are shown to be of first order, provided that the exact velocity is in H2 and the exact pressure in H1, and that the partition family of the domain is regular. ？ 1997 John Wiley & Sons, Inc.