An anti-wearing nut or bolt including a plurality of polygonal sides circumferentially formed on a head portion of the nut or bolt and; each polygonal side including: two inclined sub-sides respectively inclined outwardly convergently from opposite apexes of each polygonal side, each inclined sub-side extrapolatively defining a small biasing acute angle between each inclined sub-side and a corresponding socket side, and an intermediate sub-side transversely intersecting the two inclined sub-sides; whereby upon a clockwise or counter-clockwise rotation of the socket, one inclined sub-side of the nut or bolt will be planarly engaged with each socket side, without being linearly bitten or dogged, to thereby prevent wearing or damage of the apexes of the nut or bolt.