Stokesian dynamics simulations are presented of suspensions of sterically stabilized spheres in a viscous medium, subjected to simple shear. The steric repulsion between the grafted polymer layers of different particles is modeled using an interaction potential that is calculated using a self-consistent field lattice theory. The shear rate dependence and the volume fraction dependence of the suspension viscosity are calculated and compared to experimental data [Nommensen et al. Phys. Rev. E 59, 3147 (1999)]. It is found that shear thinning is mainly caused by the interaction contribution to the viscosity. The present paper, combined with a recent paper of Nommensen et al. [Langmuir 16, 1902 (2000)], shows that computer simulations, theoretical analysis, and experimental work give a consistent physical picture of the rheology of these suspensions when the proper interaction potential is used.