The theological behavior of a monodisperse suspension of non-Brownian particles undergoing simple shear flow in the presence of a weak interparticle force is studied using accelerated Stokesian dynamics. The availability of a faster numerical algorithm permits the investigation of larger systems (typically of 512 particles), and accurate results for the suspension viscosity, first and second normal stress differences, and the particle pressure are determined as a function of the volume fraction. The system microstructure, expressed through the pair-distribution function, is also studied and it is demonstrated how the resulting anisotropy in the pair-distribution function is correlated with the suspension non-Newtonian behavior. The ratio of the normal to excess shear stress is found to be an increasing function of the volume fraction, suggesting different volume fraction scalings for different elements of the stress tensor. The relative strength and range of the interparticle force is varied and its effect on the shear and normal stresses is analyzed. Volume fractions above the equilibrium freezing volume fraction (phi approximate to 0.494) are also studied and it is found that the system exhibits a strong tendency to order under flow for volume fractions below the hard-sphere glass transition; limited results for phi = 0.60, however, show that the system is again disordered under shear.