An analysis for hydrodynamic, non-Newtonian lubrication of misaligned journal bearings is given. The hydrodynamic load-carrying capacity for partial arc journal bearings lubricated by power-law, non-Newtonian fluids is calculated for small valves of the bearing aspect ratios. These results are compared with: numerical solutions to the non-Newtonian modified Reynolds equation, with Ocvirk’s experimental results for misaligned bearings, and with other numerical simulations. The cavitation (i.e., film rupture) boundary location is calculated using the Reynolds’ free-surface, boundary condition.