Correct prediction of cryogenic hydrogen system parameters during the chill-down stage plays a key role in ensuring its safety. During the chill-down process with liquid hydrogen, significant thermal loads occur on the structure, there is a risk of excessive pressure, flow instability, pulsations, and cavitation in pumps. The complexity of modeling the non-stationary cryogenic system chill-down process is associated not only with flow heterogeneity and the phase change of hydrogen from liquid through vapor–liquid to vapor, but also with the possibility of unstable flows with large-amplitude pulsations. Numerical modeling of such complex processes in the most complete formulation is hardly feasible. The paper presents quasi-stationary model of the chill-down process of cryogenic hydrogen systems and key assumptions. Based on the main equations of heterogeneous media mechanics, the corresponding thermohydraulic processes in a boiling hydrogen flow of variable structure are taken into account in this paper. The conceptual model of the chill-down process, features of modeling thermohydraulic processes, aspects of accounting for unsteady thermal conductivity are considered. Based on the calculations results, the key parameters of the hydrogen system chill-down at different moments in time were determined. The calculation results are compared with experimental data.