In many practical situations fluids are normally blended with additives (viscosity index improvers, viscosity thickeners, viscosity thinners) due to which they show pseudoplastic and dilatant nature which can be modelled as cubic stress model (Rabinowitsch model). The cubic stress model for pseudoplastic fluids is adopted because Wada and Hayashi have shown that the theoretical results with this model are in good agreement with the experimental results. The present theoretical analysis is to investigate the pseudoplastic effect along with the effect of rotational inertia on the pressure distribution, frictional torque and fluid flow rate of externally pressurised flow in narrow clearance between two curvilinear surfaces of revolution. The expression for pressure has been derived using energy integral approach. To analyse and discuss the effects of pseudoplasticity and fluid inertia on the pressure distribution, fluid flow rate and frictional torque, the examples of externally pressurised flow in the clearance between parallel disks and concentric spherical surfaces have been considered.