An improved flexible support for a steady bearing in rotational contact with the surface of a shaft allows the bearing and housing to substantially track the contact surface of an impeller shaft when the shaft is subject to elastic deflection during operation. The flexible support employs a flexible disc pack, which is comprised of a plurality of thin, flexible disc elements in a stacked arrangement. The disc pack is mounted to a support ring and is also mounted to the bearing housing such that the bearing housing and other bearing elements are capable of deflection to substantially align with the axis of the impeller shaft when the shaft deflects.