To provide a rolling bearing unit for supporting a vehicle wheel capable of preventing a rotation-side flange 15 from plastic deformation generated when the wheel 1 is coupled fast with the rotation-side flange 15 by tightening a nut 10, suppressing swinging of a rotor 2 coupled fast with the rotation-side flange 15, and precluding occurrence of judder at the time of applying brake.

The rolling bearing unit for supporting the wheel is structured so as to meet the condition that 6406T-1.019>Y>5790T-1.099, where T in mm is the thickness of the rotation side flange 15, and Y in MPa is the yielding stress of a metal material to constitute the flange 15. This enables suppressing a plastic deformation of the flange 15, precluding an enlargement of the swing of the rotor 2 after the wheel is replaced, and suppressing occurrence of a judder.