This paper clarifies the reasons for the main shortcomings of existing system of certification of steels and alloys in terms of their tendency to transition to a brittle state under the action of such embrittlement factors as the stress raisers (SR) and low temperatures. The main reason is the use of uninformative indicators of toughness or ductility of alloys that do not show clear thresholds for determining the brittle state; conditionality of brittleness criteria; inability to compare quantitatively the degree of embrittlement of specimens with different types of SR, $etc$. To determine the criterion of brittleness, it is proposed to apply a critical level of steel strength, $\sigma_{0.2C}$, at temperature $Т_C$, when the strength of specimen with SR, $\sigma_{NF}$, coincides with $\sigma_{0.2C}$. Ratio $\sigma_{NF}$/$\sigma_{0.2C}$ = $B_{rNF}$ is the measure of protection of specimen with SR from the transition to brittle state, and if $B_{rNF}$ < 1, then it is the measure of embrittlement by SR. Examples of application of the critical strength criterion in determining the degree of cold brittleness of steels are given, as well as in assessing the degree of embrittlement in bending tests of prismatic specimens with a fatigue crack.