We recently developed a constitutive model for magnetic dispersions by modeling the magnetic particles as rigid dumbbells dispersed in a solvent. The theory yielded a constitutive equation in which the stress tensor could be expressed as a function of the velocity gradient, an orientational order tensor, S, an average alignment vector, J, and any imposed external magnetic field, H. The constitutive equation is used here to predict material functions for steady shear flow (shear-rate dependent viscosity and first normal stress coefficient) as well as those for unsteady shear flows (stress growth upon inception of steady shear and small-amplitude oscillatory shear). The importance of effects of concentration, equilibrium nematic ordering in the dispersion, and anisotropy in the hydrodynamic drag are emphasized. Comparisons with available experimental data on viscosity for magnetic inks under steady shear flow and inception of steady shear flow show reasonably good agreement. (C) 2003 Elsevier Inc. All rights reserved.