A tripod type constant velocity universal joint, comprising: an outer joint member having three track grooves each comprising roller guide surfaces arranged so as to be opposed to each other in a circumferential direction of each of the track grooves; 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 configured to support the roller in a freely rotatable manner, the inner ring being externally fitted to each of the leg shafts, the roller being movable along the roller guide surfaces of each of the track grooves, the inner ring comprising an inner peripheral surface formed into an arc-shaped protruding surface in a longitudinal section of the inner ring, each of the leg shafts comprising an outer peripheral surface having a straight shape in a longitudinal section containing an axis of each of the leg shafts, and having a substantially elliptic shape in a cross section orthogonal to the axis of each of the leg shafts, the outer peripheral surface of each of the leg shafts being brought into abutment against the inner peripheral surface of the inner ring in a direction orthogonal to an axis of the joint, and defining a gap (m) in a direction of the axis of the joint together with the inner peripheral surface of the inner ring, wherein an outer peripheral surface of the roller is formed of a partially spherical surface having a curvature center on the axis of each of the leg shafts, wherein the roller guide surfaces are each formed of a partially cylindrical surface having a curvature center on a horizontal line (X-X) passing an intersection of a pitch circle of the track grooves and a center line of each of the track grooves, wherein a contact ratio R/r of a curvature radius R of the partially cylindrical surface of each of the roller guide surfaces to a curvature radius "r" of the partially spherical surface of the outer peripheral surface of the roller is set to satisfy 0.95≤R/r≤1.08, and wherein under a state in which no torque is applied to the joint, an end portion of the outer peripheral surface of the roller is held in abutment against the roller guide surfaces, characterized in that the roller being capable of inclining in each of the track grooves. an outer joint member having three track grooves each comprising roller guide surfaces arranged so as to be opposed to each other in a circumferential direction of each of the track grooves; 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 configured to support the roller in a freely rotatable manner, the inner ring being externally fitted to each of the leg shafts, the roller being movable along the roller guide surfaces of each of the track grooves, the inner ring comprising an inner peripheral surface formed into an arc-shaped protruding surface in a longitudinal section of the inner ring, each of the leg shafts comprising an outer peripheral surface having a straight shape in a longitudinal section containing an axis of each of the leg shafts, and having a substantially elliptic shape in a cross section orthogonal to the axis of each of the leg shafts, the outer peripheral surface of each of the leg shafts being brought into abutment against the inner peripheral surface of the inner ring in a direction orthogonal to an axis of the joint, and defining a gap (m) in a direction of the axis of the joint together with the inner peripheral surface of the inner ring, the inner ring being externally fitted to each of the leg shafts, the roller being movable along the roller guide surfaces of each of the track grooves, the inner ring comprising an inner peripheral surface formed into an arc-shaped protruding surface in a longitudinal section of the inner ring, each of the leg shafts comprising an outer peripheral surface having a straight shape in a longitudinal section containing an axis of each of the leg shafts, and having a substantially elliptic shape in a cross section orthogonal to the axis of each of the leg shafts, the outer peripheral surface of each of the leg shafts being brought into abutment against the inner peripheral surface of the inner ring in a direction orthogonal to an axis of the joint, and defining a gap (m) in a direction of the axis of the joint together with the inner peripheral surface of the inner ring, wherein an outer peripheral surface of the roller is formed of a partially spherical surface having a curvature center on the axis of each of the leg shafts, wherein the roller guide surfaces are each formed of a partially cylindrical surface having a curvature center on a horizontal line (X-X) passing an intersection of a pitch circle of the track grooves and a center line of each of the track grooves, wherein a contact ratio R/r of a curvature radius R of the partially cylindrical surface of each of the roller guide surfaces to a curvature radius "r" of the partially spherical surface of the outer peripheral surface of the roller is set to satisfy 0.95≤R/r≤1.08, and wherein under a state in which no torque is applied to the joint, an end portion of the outer peripheral surface of the roller is held in abutment against the roller guide surfaces,