To prevent a wheel disc from cracking in the vicinity of a nut means, in a fastening structure of wheels for a vehicle.

A disc 21 is fastened to a hub flange 12 by fastening the nut means 30 screwed into hub bolts 15 toward the disc 21 with the disc 21 of a wheel fitted to the hub flange 12 and with the hub bolts 15 inserted into the bolt holes 23 of the disc 21. On the disc 21, an annular clearance groove 24a is formed facing the peripheral edge on the disc side of each nut means 30. A surface area between the bolt hole 23 of the disc 21 and the clearance groove 24a functions as a receiving surface 25a to receive a fastening force by each nut means 30. The peripheral edge of each nub means 30 facing the disc is separated from the bottom surface 24x (clearance surface) of each clearance groove 24a.