Despite considerable research related to lubrication with cavitation, significant simulation results and relative comparisons remain. To accomplish that, we make use of the finite element method which is seen as a better method to simulate lubrication with cavitation models such as the variational inequality model and the Elrod-Adams model. Different techniques are used during the process of resolution by the finite element method. A penalty method is used for the variational model and an iterative method is used for the Elrod-Adams model. Finally, some simulation results are presented to show dierent aspects of the two models.