A tripod constant-velocity universal joint has three guide grooves extending axially along an outer cup, trunnions projecting from a spider inserted into the outer cup, and rollers rotatably mounted on the trunnions through rolling elements. The rollers rotate and slide against guide surfaces of the guide grooves. The rolling elements have flat end faces and are assembled into the rollers by a keystone process. The rollers have flanges for preventing dislodgement of the rolling elements from the rollers. If a distance X by which a rolling element moves radially is maximum, the ratio (W/Dn) of the width W of contact between inner side surfaces of the flanges to the diameter Dn of the rolling element is in a range of from 0% to 30%, and the height h of the flanges also is set to satisfy the ratio value (W/Dn).