The rheology of model suspensions has been characterized by standard experiments and predicted from Stokesian dynamics (SD) computer simulations. Suspensions of spherical monodisperse polystyrene latex particles (average diameter 0.45 mum) are prepared in aqueous solutions of carboxymethyl cellulose (CMC) at different concentrations and molecular weights. The rheological measurements are compared with viscosity predictions of a SD model that includes electrostatic and van der Waals forces. A new method is proposed to include boundary roughness in the SD model. The model is able to predict the correct steady shear viscosity as a function of shear rate, CMC concentration, and molecular weight. The degree of shear thinning, given by the slope of the viscosity curves, is well predicted by the model. Good quantitative agreement can be obtained if the model results are shifted along the shear rate axis by a factor of 50. The microstructural mechanisms responsible for the shear thinning are shown and described. Normal stress predictions are similar to those presented by others. The potential and limitations of the technique at the present status of its development are outlined and discussed. (C) 2001 The Society of Rheology.