An undercut free fixed type constant velocity universal joint comprising: an outer joint member having eight arcuate guide grooves extending in the axial direction in an inner spherical surface (1 a) thereof, each of said guide grooves (1 b) having a straight portion (1 c), an inner joint member having eight arcuate guide grooves extending in the axial direction in an outer spherical surface thereof, each of said guide grooves having a straight portion, eight balls disposed between the guide grooves of the outer joint member and guide grooves of the inner joint member, and a cage interposed between the outer joint member and inner joint member for retaining the balls, wherein the inner spherical surface of the cage is offset from the outer spherical surface thereof to the opposite side by an equal distance (f) in the axial direction, and wherein the outer spherical surface spherically contacts the inner spherical surface (1 a) of the outer joint member, while the inner spherical surface spherically contacts the outer spherical surface of the inner joint member, wherein center of guide grooves (1 b) of the outer joint member is offset from a joint center, and center of guide grooves of the inner joint member is offset from the joint center by equal distance to opposite sides in the axial direction, such value R1 of ratio (F/PCR) of offset amount to length of line segment linking center of guide grooves (1 b) of the outer joint member or center of guide grooves of the inner joint member and center (0 3) of balls is specified in a range of 0.069 ≤ R1 ≤ 0.121 characterized in that the relation of 0.65 ≤ B/A ≤ 0.85 is established, where A stands for the wall thickness of the cage, and B stands for the radial displacement of the balls at maximum joint angle and a contact angle (α) of the guide grooves (1b, 2b) and the balls is in a range of 29° to 40°. an outer joint member having eight arcuate guide grooves extending in the axial direction in an inner spherical surface (1 a) thereof, each of said guide grooves (1 b) having a straight portion (1 c), an inner joint member having eight arcuate guide grooves extending in the axial direction in an outer spherical surface thereof, each of said guide grooves having a straight portion, eight balls disposed between the guide grooves of the outer joint member and guide grooves of the inner joint member, and a cage interposed between the outer joint member and inner joint member for retaining the balls, wherein the inner spherical surface of the cage is offset from the outer spherical surface thereof to the opposite side by an equal distance (f) in the axial direction, and wherein the outer spherical surface spherically contacts the inner spherical surface (1 a) of the outer joint member, while the inner spherical surface spherically contacts the outer spherical surface of the inner joint member, wherein center of guide grooves (1 b) of the outer joint member is offset from a joint center, and center of guide grooves of the inner joint member is offset from the joint center by equal distance to opposite sides in the axial direction, such value R1 of ratio (F/PCR) of offset amount to length of line segment linking center of guide grooves (1 b) of the outer joint member or center of guide grooves of the inner joint member and center (0 3) of balls is specified in a range of 0.069 ≤ R1 ≤ 0.121 characterized in that the relation of 0.65 ≤ B/A ≤ 0.85 is established, where A stands for the wall thickness of the cage, and B stands for the radial displacement of the balls at maximum joint angle and a contact angle (α) of the guide grooves (1b, 2b) and the balls is in a range of 29° to 40°.