A wheel bearing apparatus comprising: an outer member integrally formed on its inner circumference with double row outer raceway surfaces (2a, 2a); an inner member including a hub wheel and at least one inner ring, the hub wheel being integrally formed on its one end with a wheel mounting flange and having a cylindrical portion axially extending from the wheel mounting flange, the inner ring being press-fitted onto the cylindrical portion of the hub wheel, the hub wheel and the inner ring being formed on their outer circumferences with double row inner raceway surfaces (4a, 5a) opposing to the double row outer raceway surfaces (2a, 2a); double row rolling elements (3, 3) contained between the inner and outer raceway surfaces (4a, 5a; 2a, 2a) of the inner and outer members (1, 2); a magnetic encoder mounted on the outer circumference of the inner ring; and annular openings formed by the inner and outer members (1, 2) being sealed by a seal mounted on the outer-side end of the outer member and by a protecting cover (10, 17, 19) mounted on the inner-side end of the outer member characterized in: that the protecting cover (10, 17, 19) is formed of non-magnetic material as having a substantially dish-shaped configuration and comprises a cylindrical fitting portion adapted to be press-fitted onto the inner circumference of the inner-side end of the outer member, a disc-shaped shielding portion (10c, 19a) extending radially inward from the fitting portion via a radially tapered portion and adapted to be closely arranged to or contacted by a sensor, and a bottom portion (10e, 19b) extending from the shielding portion (10c, 19b) via a stepped portion and covering the inner-side end of the inner member; that a flat relief portion (16, 20) is formed between the radially tapered portion and the shielding portion (10c, 19a) in parallel with the shielding portion (10c, 19a) and set slightly back from the shielding portion (10c, 19a) toward the radially tapered portion; and that an elastic member (15, 18) is integrally adhered to the outer circumference of the radially tapered portion via vulcanizing adhesion and adapted to be elastically contacted with the inner circumference of the inner-side end of the outer member. an outer member integrally formed on its inner circumference with double row outer raceway surfaces (2a, 2a); an inner member including a hub wheel and at least one inner ring, the hub wheel being integrally formed on its one end with a wheel mounting flange and having a cylindrical portion axially extending from the wheel mounting flange, the inner ring being press-fitted onto the cylindrical portion of the hub wheel, the hub wheel and the inner ring being formed on their outer circumferences with double row inner raceway surfaces (4a, 5a) opposing to the double row outer raceway surfaces (2a, 2a); double row rolling elements (3, 3) contained between the inner and outer raceway surfaces (4a, 5a; 2a, 2a) of the inner and outer members (1, 2); a magnetic encoder mounted on the outer circumference of the inner ring; and annular openings formed by the inner and outer members (1, 2) being sealed by a seal mounted on the outer-side end of the outer member and by a protecting cover (10, 17, 19) mounted on the inner-side end of the outer member characterized in: that the protecting cover (10, 17, 19) is formed of non-magnetic material as having a substantially dish-shaped configuration and comprises a cylindrical fitting portion adapted to be press-fitted onto the inner circumference of the inner-side end of the outer member, a disc-shaped shielding portion (10c, 19a) extending radially inward from the fitting portion via a radially tapered portion and adapted to be closely arranged to or contacted by a sensor, and a bottom portion (10e, 19b) extending from the shielding portion (10c, 19b) via a stepped portion and covering the inner-side end of the inner member; that a flat relief portion (16, 20) is formed between the radially tapered portion and the shielding portion (10c, 19a) in parallel with the shielding portion (10c, 19a) and set slightly back from the shielding portion (10c, 19a) toward the radially tapered portion; and that an elastic member (15, 18) is integrally adhered to the outer circumference of the radially tapered portion via vulcanizing adhesion and adapted to be elastically contacted with the inner circumference of the inner-side end of the outer member. that the protecting cover (10, 17, 19) is formed of non-magnetic material as having a substantially dish-shaped configuration and comprises a cylindrical fitting portion adapted to be press-fitted onto the inner circumference of the inner-side end of the outer member, a disc-shaped shielding portion (10c, 19a) extending radially inward from the fitting portion via a radially tapered portion and adapted to be closely arranged to or contacted by a sensor, and a bottom portion (10e, 19b) extending from the shielding portion (10c, 19b) via a stepped portion and covering the inner-side end of the inner member; that a flat relief portion (16, 20) is formed between the radially tapered portion and the shielding portion (10c, 19a) in parallel with the shielding portion (10c, 19a) and set slightly back from the shielding portion (10c, 19a) toward the radially tapered portion; and that an elastic member (15, 18) is integrally adhered to the outer circumference of the radially tapered portion via vulcanizing adhesion and adapted to be elastically contacted with the inner circumference of the inner-side end of the outer member.