For the life prediction and fatigue failure prevention of the constant velocity joint, the maximum equivalent stress and its location in depth from the contact area are essential. These values give the fundamental information to determine the depth of the surface hardening treatment at the contact area. Contact stresses are evaluated at the surface and subsurface of the ball groove of the Weiss type constant velocity joint. The maximum contact pressure and the maximum equivalent stress are obtained. The effects of various parameters such as the radius of ball groove, friction coefficient, and residual stress are studied. The maximum equivalent stress and the maximum contact pressure increase as the radius of the ball grove increases. The location of the maximum equivalent stress moves toward surface as the friction coefficient increases. It was also found that the maximum equivalent stress becomes minimum when the compressire residual stress is about 0.16 times of the maximum contact pressure.