A procedure for solving the Navier-Stokes equations for the steady, three-dimensional flow of a non-Newtonian fluid within a finite-breadth hydrodynamic journal bearing is described. The method uses a finite-difference approach, together with a technique known as SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) which has now become established in the field of computational fluid dynamics. The concept of ‘effective viscosity’ to describe the non-linear dependence of shear stress on shear rate is used to predict the performance of bearings having a single full-width axial inlet groove situated at the position of maximum film thickness. To illustrate the capabilities of the procedure, results are obtained for a range of non-linearity factors, and lead to the conclusion that the pressure distribution, attitude angle, end-leakage rate, shear force and load capacity can all be predicted for a variety of non-Newtonian lubricants using the SIMPLE numerical integration technique.