By coupling the equations of the modified Reynolds equation with the anisotropic slip effect, the piezoviscosity and piezodensity relations, the elasticity deformation equation, and the load equilibrium equation are solved simultaneously using the finite element method (FEM) for the elastohydrodynamic lubrication (EHL) of circular contact problems under constant load conditions. Results show that the film thickness is more sensitive to the slip length in a sliding direction (x-direction) than to the slip length in a transverse direction (y-direction). A slip in the y-direction concentrates the pressure toward the center region, and the film collects toward the central region and possesses a deeper dimple. The central pressure and coefficient of friction (COF) increase as the slip length in the y-direction increases. On the contrary, the central pressure and COF decrease as the slip length in the x-direction increases. Detailed results and animations for film thicknesses and pressure distributions are available under the “Supplemental Data” tab for this paper on the ASME Digital Collection.