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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.