We report a Brownian configuration field implementation of a recent constitutive equation for suspensions. reported by Phan-Thien et al. 1999. The numerical method is a hybrid technique, which combines a modification of the Brownian configuration field method described by Hulsen et al. 1997 and the adaptive viscosity split stress formulation proposed by Sun et al. 1996. The implementation is used to examine the flow past a sphere in a tube. The relative viscosity derived from the drag force/sedimentation velocity agrees well with a well-known empiricism, In addition, the ratio of the pressure force to the drag on the sphere seems to be weakly dependent on the volume fraction, and is somewhat higher than Brenner's results of 1962, which were derived for Newtonian fluids.