Abstract: An improved lock nut adapted for repeated use in locking onto a series of bolts, each time compressively gripping the bolt with substantially the same high compressive force. In one embodiment, the locking is achieved by a plurality of resilient locking beams that flex radially outwardly to accommodate the bolt, while in another embodiment, the locking is achieved by a generally oval-shaped sleeve that flexes into a more circular shape when the bolt is threaded into it. In both embodiments, the flexing is made to occur at multiple locations along the beam's (or sleeve's) length by providing a stepped radial thickness, such that the total amount of elastic flexing can be maximized. In another feature of the invention, usable in the embodiment that includes the multiple locking beams, the axial slots separating the beams are defined by beam side walls that diverge from each other by an amount that increases from substantially zero at the bases of the beams to a maximum at the remote tips of the beams.