Hydrodynamic lubrication takes a fundamental role in mechanical systems to reduce energy losses and prevent mechanical breakdown. In order to model hydrodynamic lubrication in thin films the solution of the Reynolds equation is required. However, the Reynolds equation cannot re ect all the lubricant characteristics in thin films. The effects of two critical factors, wall slip and cavitation, need to be considered. A new numerical solution of the Reynolds equation is presented to model two-dimensional hydrodynamic lubrication, including the linear complementary mass-conserving cavitation model and multi-linearity wall slip model. In addition, a new wall slip model has been proposed by modifying the multi-linearity wall slip model to make it more computationally affordable. The proposed mathematical model has been validated against available models in literature with the tests performed on journal bearings, slider bearings, squeeze dampers, and surface textured bearings. The proposed novel wall slip model is up to 9 times more computational affordable than the original multi-linearity wall slip model.