In accordance with the present invention, use is made of the adjacent vertically arranged fuel bundles which surround the empty core position to be filled with the fuel bundle to be inserted. Such use of the adjacent bundles involves the placement upon the top tie plate of each bundle of a separate and individual centering device, each centering device being of a generally box-like cap configuration and engaging the upper tie plate of each fuel bundle. Preferably, each such centering device includes a pair of tapered dowel pins which engage apertures formed in the upper surface of the fuel assembly tie plate so that lateral forces imposed upon the centering device will be transmitted to the upper end of the fuel bundle assembly that may be bowed into the empty core position. Each centering device also preferably includes an elongated handling pole uniquely connected to the top wall of the centering device so that each centering device may be lowered individually onto the upper tie plate of its respective associated fuel bundle. This elongated handling pole engages the top wall of the centering device through a novel ball and socket arrangement which permits the handling of the pole to swing well clear of the fuel insertion operating area after the centering device has been placed on its respective fuel bundle. The unique ball and socket arrangement also allows the centering device to self-align itself on the handling pole when the handling pole is lifted vertically or, alternatively, being lowered down on top of the fuel bundle during installation thereon.