A constant-velocity joint includes an outer ring formed with a bore defined by six flat surfaces parallel to its axis, and a trunnion member received in the bore of the outer ring. The trunnion member has an outer periphery formed with three first spherical surfaces circumferentially spaced apart from each other and three second spherical surfaces circumferentially spaced apart from each other and each disposed between adjacent first spherical surfaces. Each first spherical surface is in contact with one of the flat surfaces at a point offset from the circumferential center of the flat surface in one circumferential direction. Each second spherical surface is in contact with another flat surface at a point offset from the circumferential center of the flat surface in the other circumferential direction. At least one of the outer ring and the trunnion member is made of a synthetic resin.