A model-based evaluation procedure by a trap-diffusion integrated finite element model (FEM) is used to interpret the experimentally measured thermal desorption spectra (TDS) of Fe-C-Ti alloys. Two material conditions are compared, i.e. as-quenched vs. quenched and tempered, in which TiC have precipitated. The discrepancy between measurement and simulation is found to be very small for all material conditions. The model shows high trapping energies of around 58 kJ/mol to 110 kJ/mol (0.61 eV–1.14 eV), when the materials are tempered. These traps could be related to carbon vacancies in TiC precipitates. Display omitted •A model-based evaluation procedure is successfully applied to measured TDS of the Fe-C-Ti alloy.•A spectrum of five trapping energies is related to corresponding microstructure.•TiC carbides trap hydrogen mainly at the interface.•The appropriateness of Oriani's trapping model is verified.