In a wheel-support rolling bearing unit, in order to made a flange 6 thinner and thus lighten the bearing unit without impairing fatigue strength, machinability, and workability after forging, the composition of the alloy steel constituting the flange attached member (hub ring 2), the surface hardness of the root portion 14 on the axial outside surface side of the flange 6, and the surface roughness, are stipulated to thereby improve the durability ratio (fatigue limit strength/tensile strength) of the flange 6. In one aspect, the member is made from an alloy steel containing C: 0.5 to 0.65 weight %, Mn: 0.3 to 1.5 weight %, Si: 0.1 to 1.0 weight %, Cr: 0.01 to 0.5 weight %, S: 0.35 weight % or less, and any one type or more selected from 0.01 to 0.2 weight % of V, 0.01 to 0.15 weight % of Nb, and 0.01 to 0.15 weight % of Ti, with the rest being Fe and inevitable impurities, and the oxygen contents is 15 ppm or less. Moreover, the surface hardness of the inner raceway 7a formed with the hardened layer, is between Hv 650 and 780, and the surface hardness of a portion not formed with the hardened layer is between Hv 230 and 300.