A tripod type constant velocity universal joint, comprising: an outer joint member comprising three track grooves each formed so as to have roller-guide surfaces arranged to face each other in a circumferential direction of the outer joint member; a tripod member comprising three leg shafts projecting in a radial direction of the tripod member; and roller units each comprising a roller and an inner ring for supporting the roller in a freely rotatable manner, the inner ring being externally fitted to corresponding one of the three leg shafts, the roller being movable along the roller-guide surfaces of corresponding one of the three track grooves, an inner peripheral surface of the inner ring being formed into a convex circular-arc shape in a vertical cross-section comprising an axial line of the ring, an outer peripheral surface of each of the three leg shafts being formed into a straight shape in vertical cross-section comprising an axial line of a corresponding one of the three leg shafts, each of the three leg shafts being formed into a substantially elliptical shape in a horizontal cross-section that is orthogonal to an axial line of the corresponding one of the three leg shafts, a major axis (a) of the substantially elliptical shape being formed in a direction that is orthogonal to an axial line of the tripod type constant velocity universal joint, the outer peripheral surface of each of the three leg shafts being held in contact with the convex circular-arc shape of the inner peripheral surface of a corresponding one of the inner rings in the direction that is orthogonal to the axial line of the tripod type constant velocity universal joint, a minor axis (b) of the substantially elliptical shape being formed in a direction of the axial line of the tripod type constant velocity universal joint, the outer peripheral surface of each of the three leg shafts and the inner peripheral surface of the corresponding one of the inner rings having a clearance (m) formed therebetween in the direction of the axial line of the tripod type constant velocity universal joint, characterized in that each of the three leg shafts comprising an outer peripheral surface region comprising the major axis (a) of the substantially elliptical shape that is finished through grinding and held in contact with the inner peripheral surface of the corresponding one of the inner rings, and each of the three leg shafts comprising a grinding relief portion formed at an end portion in the circumferential direction of the outer peripheral surface region, wherein the grinding relief portion is positioned outside the range where the inner peripheral surface of the corresponding one of the inner rings and the outer peripheral surface region are held in contact with each other. an outer joint member comprising three track grooves each formed so as to have roller-guide surfaces arranged to face each other in a circumferential direction of the outer joint member; a tripod member comprising three leg shafts projecting in a radial direction of the tripod member; and roller units each comprising a roller and an inner ring for supporting the roller in a freely rotatable manner, the inner ring being externally fitted to corresponding one of the three leg shafts, the roller being movable along the roller-guide surfaces of corresponding one of the three track grooves, an inner peripheral surface of the inner ring being formed into a convex circular-arc shape in a vertical cross-section comprising an axial line of the ring, an outer peripheral surface of each of the three leg shafts being formed into a straight shape in vertical cross-section comprising an axial line of a corresponding one of the three leg shafts, each of the three leg shafts being formed into a substantially elliptical shape in a horizontal cross-section that is orthogonal to an axial line of the corresponding one of the three leg shafts, a major axis (a) of the substantially elliptical shape being formed in a direction that is orthogonal to an axial line of the tripod type constant velocity universal joint, the outer peripheral surface of each of the three leg shafts being held in contact with the convex circular-arc shape of the inner peripheral surface of a corresponding one of the inner rings in the direction that is orthogonal to the axial line of the tripod type constant velocity universal joint, a minor axis (b) of the substantially elliptical shape being formed in a direction of the axial line of the tripod type constant velocity universal joint, the outer peripheral surface of each of the three leg shafts and the inner peripheral surface of the corresponding one of the inner rings having a clearance (m) formed therebetween in the direction of the axial line of the tripod type constant velocity universal joint, characterized in that each of the three leg shafts comprising an outer peripheral surface region comprising the major axis (a) of the substantially elliptical shape that is finished through grinding and held in contact with the inner peripheral surface of the corresponding one of the inner rings, and each of the three leg shafts comprising a grinding relief portion formed at an end portion in the circumferential direction of the outer peripheral surface region, wherein the grinding relief portion is positioned outside the range where the inner peripheral surface of the corresponding one of the inner rings and the outer peripheral surface region are held in contact with each other.