in a tripod type constant velocity joint , in order to produce a recovery couple to correct the inclination of the rolling direction of a roller and to reduce surface pressure without using angular contact provided by a gothic arch - shaped roller guide surface , it is arranged that where r1 and r2 are the minimum and maximum values , respectively , of the radius of curvature of the generatrix for the outer peripheral surface of the roller within the range where solid contact is effected by elastic deformation of the contact section between the roller and the roller guide surface under a predetermined torque load with respect to the radius of curvature of the roller guide surface , the radius of curvature of the generatrix be set in the range r1 ≦ r ≦ r2 .