In this paper we calculate numerically the shear induced distortion of the equilibrium microstructure in a dilute colloidal suspension. In the low density limit, our predictions both with and without hydrodynamic interactions follow the form of the Ree–Eyring equation for the shear rate dependence of the rheology. For low to intermediate shear rates, rescaling the low density solutions by appropriate volume fraction dependent scale factors captures many of the qualitative features observed in simulation and experiment on systems at high concentration, including shear thinning and normal stresses. At high shear rates, more detailed consideration of many-particle interactions are required to account for the observed phenomenology and the use of the mean-field approximation inherent in the rescalings fails. Comparison of systems with and without hydrodynamic interactions suggests that both hydrodynamic and thermodynamic forces act to increase the stress relaxation time in concentrated suspensions.