The rheological material functions predicted by a previously selected constitutive equation (CE) for discotic mesophases are presented. The predicted relations among rheological properties, shear-induced microstructure, processing conditions and material parameters of discotic mesophases are characterized and discussed. The first and second normal stress differences corresponding to planar (i.e., 2-D orientation) microstructure mode of discotic nematics are found to be qualitatively similar to those for rod-like nematics despite the existing differences in flow-orientation characteristics. The first (second) normal stress difference for discotic mesophases corresponding to nonplanar (i.e., 3-D orientation) microstructure mode is always positive (positive or negative depending on viscous effects) and is found to be due to flow-induced biaxiality. The effect of change in nematic potential (or temperature) on rheological properties of discotic mesophases is also presented. The apparent shear viscosities for various microstructure modes and material properties are also presented and shown to agree qualitatively with the available experimental data. Though only restricted validation of the predicted results with the actual experimental data of discotics is possible, the present study provides essential theoretical feedback to the on-going experimental work being pursued in understanding the processing behavior of mesophase pitches.