This paper presents a comprehensive nonlinear numerical analysis of the flow modeling of mesophase pitches performed using a previously formulated mesoscopic viscoelastic theological theory (Singh and Rey (2000)) that takes into account short-range order elasticity, long range elasticity, and flow-induced texture transformations. A complete extra stress tensor equation is developed from first principles for liquid crystal materials under nonhomogeneous arbitrary flow. This mesoscopic viscoelastic model has been adapted to describe the theology of flow-aligning thermotropic discotic nematic liquid crystals as models of mesophase pitches. Predictions for simple shear flow (under nonhomogeneous conditions) for the shear viscosity, first normal stress differences, and transient shear stress are presented. The accuracy of the numerical results is established by a thorough validation procedure based on [Cato et al. (2004)], which is the companion paper, and permit to validate this mesoscopic viscoelastic theory as model of liquid crystalline mesophase pitch. Very good qualitatively agreement between experiments and simulations is found for all theological characterizations. (C) 2005 The Society of Rheology.