The problem of predicting the behavior of structural materials in hydrogen-bearing media (including extreme operating environments) cannot be solved without a thorough understanding of the mechanisms of hydrogen accumulation and transfer inside these materials. This issue is especially pressing for hydride-forming materials, such as widely used titanium alloys. Titanium and its alloys are used, in particular, in designing power and chemical reactors, for the geological disposal of highly radioactive waste. The paper presents a nonlinear mathematical model of hydrogen permeability taking into account the possible formation of hydride phases (after certain concentrations of dissolved atomic hydrogen are attained), and the iterative method for solving the corresponding boundary value problem based on implicit difference schemes.