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 mathematical model taking into account the dynamics of sorption-desorption processes and reversible capture of diffusing hydrogen by inhomogeneity of the material’s structure, and also modification of the model when the transport rate is high. The results of numerical modelling allow to obtain information about output data sensitivity with respect to variations of the material’s hydrogen permeability parameters. Furthermore, it is possible to analyze the dynamics of concentrations and fluxes that cannot be measured directly. Experimental data for Ta77Nb23 and V85Ni15 alloys were used to test the model. This work is supported by the Russian Foundation for Basic Research (Project No. 15-01-00744).