Abstract: When the components of hip prostheses move a sufficient distance laterally to contact the edge of the acetabular cup, causing abnormally high contact stresses, the contact dimensions and maximal contact pressure with appropriate edge radius were investigated based on classical Hertzian contact theory. The computational results show that with the increase of the edge radius of the hip, the angle of acetabulum within the range of 2°-55° first decreases slightly, then slowly increases, and eventually tends to be stable to obtain the minimal contact pressure. While the angle over 50° contact pressure increases rapidly and the large change of edge radius of hip is needed to obtain the minimal contact pressure. With the change of the acetabulum angle, the radius of the pressure edge decreases first and then reaches a minimum, and there is a sharp increase after reaching 45°. The edge radius of hip bearings is designed to find contact size and the maximum contact pressure are proportional to loading under the same condition. The increased angle of cup inclination reduces contact size while enlarges the maximum contact pressure. The appreciate radius using this contact theory better resist severe edge loading contact stresses for reducing the stripe wear. This can prolong the lifetime of the hip prostheses.