A tripod constant velocity universal joint includes among others an inner joint member having a boss 22 and journals 24 radially protruding from the boss, a radius of curvature R1 as viewed in a cross section of a journal bottom part 23 connecting the boss 22 to the journal 24 and as measured at opposing locations in a circumferential direction of the joint is larger than a radius of curvature R2 of the journal bottom part as viewed in its cross section and as measured at opposing locations in an axial direction of the joint and R1 gradually decreases down to R2.