An approach for numerical investigation of mixed lubricated systems is presented in this article. By means of the Finite Element Method, a two dimensional model is built and composed of one fluid lubricating two sliding rough surfaces. The challenge of such a model resides in the complexity of interactions between the fluid and the solid structure. The used meshing method called Coupled-Eulerian-Lagrangian is utilized for high contact topology changes, a phenomenon occurring in case of large translation of rough surfaces in contact with another viscous body. A model based on a two dimensional axial bush bearing is developed in order to evaluate the abilities of such an approach in calculating a contact pressure and the fric-tion coefficient between both lubricated solids. The main friction coefficient is separated into solid-solid and fluid-solid friction part. The present approach gives the opportunity to identify the influence parameters on the tribo-logical behaviour of mixed friction systems.