The analysis of hydrodynamic bearings using non-Newtonian lubricants being presented in this paper is with a distinctly different approach. By integral averaging of the shear strain rate across the film, an averaged viscosity, which is only a function of the coordinates along the film, has been defined. This makes it possible to apply the usual form of Reynolds equation. The steady-state pressure distribution is established by an iteration scheme which refines the viscosity field in successive steps. The performance characteristics results obtained from the analysis for a plane journal bearing with non-Newtonian lubricant following cubic shear stress law, compare very well with the experimental and theoretical results available in the published literature.