An analysis using computational modeling by finite elements of the phenomenon of elastohydrodynamic lubrication (EHL) was carried out for a transmission system of pinion gear in a crankcase with partial filling lubrication. The analysis utilized tribological studies describing the contact behavior characteristics of solid surfaces with the lubrication film caused by dragging and splashing. Furthermore, the characteristics of the Reynolds-Hertz model for this type of phenomena are described, as well as the equations of elastic deformation and elastic displacements along with the geometry of the non-concordant bodies in contact. This was done by modeling the Lagrangian-Eulerian type for non-Newtonian fluid, implementing multiphysics coupling methods. The pressure profile of the lubricant films, the temperature reached by the lubricant, and the von Mises stress at the contact were obtained, showing a good approximation with the related results, indicating a range of 30 MPa to 900 MPa of pressure in the lubricant film and von Mises stress ranging from 30 MPa to 100 MPa in the contact area of the gear tooth.