A constant velocity universal joint, comprising: an outer joint member having an inner surface provided with track grooves ; an inner joint member having an outer surface provided with track grooves ; torque transmitting balls arranged in torque transmitting ball tracks formed in cooperation between the track grooves of the outer joint member and the track grooves of the inner joint member , the track grooves of the inner joint member corresponding to the track grooves of the outer joint member ; and a cage for holding the torque transmitting balls , wherein at least one of each of the track grooves of the outer joint member and each of the track grooves of the inner joint member is formed by cold-forging finishing, characterized in that a range of a track groove bottom side that is needed for shape management of the at least one of the each of the track grooves of the outer joint member and the each of the track grooves of the inner joint member is formed into a Gothic arch shape in horizontal cross-section, functionally required ranges, in which the torque transmitting balls make contact with the track grooves, of track groove opening sides of the at least one of the each of the track grooves of the outer joint member and the each of the track grooves of the inner joint member are each formed into an elliptical, non-circular, shape in horizontal cross-section, and a continuous position between the Gothic arch shape and the elliptical shape is located on a groove opening side within a range of from 20° to 45° with respect to a straight line (L) connecting a ball center (Ob) and a track groove bottom center. an outer joint member having an inner surface provided with track grooves ; an inner joint member having an outer surface provided with track grooves ; torque transmitting balls arranged in torque transmitting ball tracks formed in cooperation between the track grooves of the outer joint member and the track grooves of the inner joint member , the track grooves of the inner joint member corresponding to the track grooves of the outer joint member ; and a cage for holding the torque transmitting balls , wherein at least one of each of the track grooves of the outer joint member and each of the track grooves of the inner joint member is formed by cold-forging finishing, characterized in that a range of a track groove bottom side that is needed for shape management of the at least one of the each of the track grooves of the outer joint member and the each of the track grooves of the inner joint member is formed into a Gothic arch shape in horizontal cross-section, functionally required ranges, in which the torque transmitting balls make contact with the track grooves, of track groove opening sides of the at least one of the each of the track grooves of the outer joint member and the each of the track grooves of the inner joint member are each formed into an elliptical, non-circular, shape in horizontal cross-section, and a continuous position between the Gothic arch shape and the elliptical shape is located on a groove opening side within a range of from 20° to 45° with respect to a straight line (L) connecting a ball center (Ob) and a track groove bottom center. <EOS>