A triplan constant velocity universal joint (22) having an annular outer member (24), an inner member (26), three pairs of shoes (28) and three sets of four elongated rollers (30). The interior cavity (32) of the outer member (34) has three longitudinal lobes (36) forming opposing pairs of parallel longitudinal guideways (38) which mate with the elongated rollers (30). The inner member (26) is centrally positioned within the outer member (24) and has three trunnions (40), each extending radially into a respective one of the three longitudinal lobes (36). Each trunnion (40) has an associated pair of shoes (28). Both the trunnion (40) and its shoes (28) have mating truncated spherical surfaces (46) which permit the shoes (28) to pivot relative to the trunnion (40). The elongated rollers (30) are retained within longitudinal raceways (52) provided along the surface of each shoe (28) opposite its spherical surface (46). The elongated rollers (30) engage an adjacent longitudinal guideway (38) on either side of its trunnion (40). The elongated rollers (30) have barrel-shaped contours which mate with the contour of the bearing surfaces (48) and with the contour of their adjacent guideways (38) so as to provide line contact between the elongated rollers (30), the longitudinal bearing surface (48) and the adjacent guideways (38).