steel on the critical temperature of brittleness T c for specimens with an annular notch in tension or pre-cracked specimens in three-point bending are considered. As shown, the excessive (supercritical) low-temperature hardening of steel, unbalanced with the required margin of its toughness, when real strength of the steel, σ 0.2 , exceeds critical strength for a given type of SR, σ 0.2c , is the reason for brittleness of specimens with SR. Physical essence of the quantity σ 0.2c is explained in terms of specific characteristics of the steel resistance to break, B r , reflecting its margin of toughness. Recommendations are formulated for optimising a set of mechanical properties for products such as fastening bolts with SR in the form of a screw thread, to prevent their cold brittleness during low-temperature operation.