Metals that are exposed to high pressure hydrogen gas may undergo detrimental failure by embrittlement. Understanding the mechanisms and driving forces of hydrogen absorption on the surface of metals is crucial for avoiding hydrogen embrittlement. In this study, the effect of stress-enhanced gaseous hydrogen uptake in bulk metals is investigated in detail. For that purpose, a generalized form of Sievert's law is derived from thermodynamic potentials considering the effect of microstructural trapping sites and multiaxial stresses. This new equation is parametrized and verified using experimental data for carbon steels, which were charged under gaseous hydrogen atmosphere at pressures up to 1000 bar. The role of microstructural trapping sites on the parameter identification is critically discussed. Finally, the parametrized equation is applied to calculate the stress-enhanced hydrogen solubility of thin-walled pipelines and thick-walled pressure vessels during service. Display omitted •Improvement of Sievert's law to consider trapping sites and stress states.•Calculation and validation of gaseous hydrogen solubility under extreme conditions.•Hydrogen uptake measured for L450 steel at 200 and 1000 bar.•Calculation of the hydrogen solubility in pipes and pressure vessels.•Comprehensive literature survey of gaseous hydrogen solubility.