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This paper considers modeling the flow with cavitation in a fluid film bearing. In typical bearings, the film thickness is small in comparison with the length, which reduces the Navier-Stokes equations into the Reynolds equation. To keep the minimum pressure at the cavitation limit, the problem is represented as a variational inequality. For numerical solutions, the variational problem is transformed into a penalty problem and discretized with the finite element method. Comparison of the numerical results with the experimental data shows that the pressure profiles are similar. However, the numerical results overestimate the cavitation region found in the experimental data.