The advancement of modern processors with many-core and large-cache may have little computational advantages if only serial computing is employed. In this study, several parallel computing approaches, using devices with multiple or many processor cores, and graphics processing units are applied and compared to illustrate the potential applications in fluid-film lubrication study. Two Reynolds equations and an air bearing optimum design are solved using three parallel computing paradigms, OpenMP, Compute Unified Device Architecture, and OpenACC, on standalone shared-memory computers. The newly developed processors with many-integrated-core are also using OpenMP to release the computing potential. The results show that the OpenACC computing can have a better performance than the OpenMP computing for the discretized Reynolds equation with a large gridwork. This is mainly due to larger sizes of available cache in the tested graphics processing units. The bearing design can benefit most when the system with many-integrated-core processor is being used. This is due to the many-integrated-core system can perform computation in the optimization-algorithm-level and using the many processor cores effectively. A proper combination of parallel computing devices and programming models can complement efficient numerical methods or optimization algorithms to accelerate many tribological simulations or engineering designs.