Cavitation can occur in both static and dynamically loaded journal bearings. A numerical solution of this two-phase flow problem suffers from the difficulties of having to solve different governing equations within the full and cavitated zones, and of not knowing the boundary between these two regions. For Newtonian fluids an efficient numerical algorithm which addresses these problems has been proposed by Elrod. We have extended the Elrod algorithm to also cover non-Newtonian fluids and implemented it in an axially symmetric finite journal bearing. For a Newtonian lubricant, under isothermal conditions, both static and dynamic loading cases have been solved. For the non-Newtonian case, a generalized Reynolds equation has been derived. This equation has been solved (under static loading) for a particular shear thinning Generalized Newtonian Fluid. Predictions compare favorably with existing literature.