This work ddresses the applicability of a local criterion incorporating the coupling of critical stress and a critical hydrogen concentration to predict hydrogen embrittlement effects on the fracture strength of high strength steels using notched round specimens with different notch root radii. The numerical simulations incorporating a relatively simple hydrogen transport model provide strong support to the adoption of a failure criterion in terms of achieving a critical level of tensile stress coupled to the local hydrogen concentration, which, in turn, enable the construction of a failure locus for the material. For the cases analyzed here, construction of such a failure locus based on a critical combination of maximum principal stress and hydrogen concentration enabled predictions of fracture strength for hydrogen-charged tensile specimens which are in very good agreement with experimental data. Overall, the results presented here lend additional support for further developments of a local stress-based criterion to predict hydrogen embrittlement effects on the fracture strength of high strength steels.