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 respectively with double row inner raceway surfaces (4a, 5a) opposing to the double row outer raceway surfaces (2a, 2a); double row rolling elements (3, 3) freely rollably contained between the inner raceway surfaces (4a, 5a) and outer raceway surfaces (2a, 2a) of the inner member and outer member; a pulser ring fitted onto the outer circumference of the inner ring; a seal mounted on the outer-side end of the outer member and a protecting cover mounted on the inner-side end of the outer member in order to close and seal annular openings formed between the outer member and the inner member at their both ends; and the protecting cover being formed of non-magnetic steel sheet as having a cup-shaped configuration by press working and comprises a cylindrical fitting portion press-fitted into the inner circumference of the inner-side end of the outer member, a disc-shaped shielding portion extending radially inward from the fitting portion via a radially reducing portion and the inner-side surface of the shielding portion being adapted to be arranged closely to or in contact with a rotation speed detecting sensor, and a bottom portion continuous to the shielding portion via a stepped portion to close the inner-side end of the inner member; characterized in: that a full deflection of the side surface of the shielding portion caused by a load same as that applied to the protecting cover when it is press-fitted into the outer member is limited to a predetermined value or less, wherein the allowable limitation of the full deflection of the shielding portion of the protecting cover is 0.15 mm or less, and wherein the shielding portion of the protecting cover is formed so that it is inclined toward the outer-side by a predetermined inclined angle (θ) such that the radially inward end of the shielding portion is closer to the outer-side. 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 respectively with double row inner raceway surfaces (4a, 5a) opposing to the double row outer raceway surfaces (2a, 2a); double row rolling elements (3, 3) freely rollably contained between the inner raceway surfaces (4a, 5a) and outer raceway surfaces (2a, 2a) of the inner member and outer member; a pulser ring fitted onto the outer circumference of the inner ring; a seal mounted on the outer-side end of the outer member and a protecting cover mounted on the inner-side end of the outer member in order to close and seal annular openings formed between the outer member and the inner member at their both ends; and the protecting cover being formed of non-magnetic steel sheet as having a cup-shaped configuration by press working and comprises a cylindrical fitting portion press-fitted into the inner circumference of the inner-side end of the outer member, a disc-shaped shielding portion extending radially inward from the fitting portion via a radially reducing portion and the inner-side surface of the shielding portion being adapted to be arranged closely to or in contact with a rotation speed detecting sensor, and a bottom portion continuous to the shielding portion via a stepped portion to close the inner-side end of the inner member; characterized in: that a full deflection of the side surface of the shielding portion caused by a load same as that applied to the protecting cover when it is press-fitted into the outer member is limited to a predetermined value or less, wherein the allowable limitation of the full deflection of the shielding portion of the protecting cover is 0.15 mm or less, and wherein the shielding portion of the protecting cover is formed so that it is inclined toward the outer-side by a predetermined inclined angle (θ) such that the radially inward end of the shielding portion is closer to the outer-side.