A numerical scheme that has been successfully used to solve a wide variety of compressible flow problems, including flows with large and small discontinuities, entitled the space-time conservation element and solution element (CE/SE) method, is extended to compute compressible viscous flows in pressurized thin fluid films. This method is applied to calculate the pressure distribution in a hybrid gas journal bearing. The formulation of the problem is presented, including the modeling of the feeding system. The numerical results obtained are compared with experimental data. Good agreement between the computed results and the test data were obtained, and thus, validate the CE/SE method to solve such problems.