Abstract: A method for removing broken fasteners so as to render the broken shank readily removable from a tapped hole in a machine part after a shear-type fracture of the fastener shank. In one illustrated form the fastener is a hexhead machine bolt having uniformly spaced slots cut into the shank from one end thereof to the other and filled with a lubricant material prior to installation. After a shear-type fracture a tool having axial projections at one end thereof mating with the slots is inserted into the interstices formed by the slots in the periphery of the sheared-off shank portion to force lubricant into the threads and to provide reaction surfaces to enable use of the tool to turn the shank portion out of the tapped hole. A second illustrated embodiment of the fastener shows an Allen head stud similarly slotted.