Abstract: A simple and useful technique was developed to solve the problem of the isothermal elastohydrodynamic lubrication (EHL) of elliptical point contacts with two arbitrary surface velocities. Thus a mathematical model for the isothermal EHL with non-Newtonian lubrication of the elliptical contact was proposed, by taking into account the two surface velocities in the same and opposite directions or each at an arbitrary angle to the minor axis of the contact ellipse. The numerical isothermal solutions were obtained and the results were discussed. It was found that the directions of the combined entrainment velocity varied with varying directions of the two surface velocities, while the slanting angle of the contact ellipse within the calculation field also varied therewith. Moreover, since the contact ellipse was proportional to the coordination axis at a certain angle, the pressure and thickness of the oil film was no longer asymmetric with respect to the Y=0 plane. Namely, the second pressure peak and the oil film neck shrinkage appeared at the exit in the Y=0 plane, while the second pressure peak and the oil film neck shrinkage appeared at the inlet in the X=0 plane.