A bearing apparatus is provided for a wheel of vehicle which can increase the strength and durability of the hub wheel (1) under the condition of rotary bending. It comprises an outer member (5) formed with double row outer raceway surfaces (5a) on the inner peripheral surface thereof, an inner member (1) formed with double row inner raceway surfaces (1a) arranged oppositely to the double row outer raceway surfaces (5a), double row rolling elements (7) contained freely rollably between the outer and inner raceway surfaces respectively of the outer and inner members, and a wheel mounting flange (10) formed integrally with either one of the outer member (5) or the inner member and is characterized in that at least one of the outer member (5) and the inner member (1) on which the wheel mounting flange (10) is formed is heat treated and their raceway surfaces are hardened by quenching to a predetermined surface hardness.