A sealing apparatus (20) has a slinger (22) with a substantially L-shaped cross-section including a cylindrical portion (22a) to be fitted on a member of rotational side and an upstanding portion (22b) radially extending from one end of the cylindrical portion (22a). The apparatus also has a core member (23a) of a substantially L-shaped cross-section including a cylindrical portion (23aa) to be fitted in a member of stationary side and an upstanding portion (23ab) radially extending from one end of the cylindrical portion. Further included is a sealing element (23b) including one ore more side lips (23ba) and (23ba) adapted to be slidably contacted with the upstanding portion (22b) of the slinger (22) and one or more radial lips (23bb) adapted to be slidably contacted with the cylindrical portion (22a) of the slinger (22). An interference of a portion of the cylindrical portion (23aa) and/or (22a) of the core member (23a) and/or the slinger (22) near the upstanding portion (23ab) and/or (22b) is formed smaller than that of the other portion of the cylindrical portion (23aa) and/or (22a) of the core member (23a) and/or the slinger (22).