High-purity hydrogen is required for clean energy and a variety of chemical technology processes. Different alloys, which may be well-suited for use in gas-separation plants, were investigated by measuring specific hydrogen permeability. One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones), and identify the limiting factors. This paper presents a nonlinear model of hydrogen fast permeability in accordance with the specifics of the experiment and parametric identification algorithm. This work is supported by the Russian Foundation for Basic Research (Project No. 15-01-00744).