An approximate solution of the “critical” maximum compressive stress present in rolling contact fatigue is given. Geometries normally used in rolling contact rig tests having contact areas varying from rectangular to full elliptical contact are considered. For cylinders in contact it is shown that the first order solution for end of contact stress is considerably above the nominal line contact Hertz stress usually calculated. Confirmation of the approximate stresses calculated is provided by deformation studies just into the plastic regime, and rolling contact fatigue tests on both cylindrical and 100-inch radius toroidal specimen rollers. Contributed by the ASLE Technical Committee on Bearings and Bearing Lubrication and presented at the Annual Meeting of the American Society of Lubrication Engineers held in New York, April, 1963.