The paper considers the hydrogen diffusion into metals from their external environment. In order to properly describe a time-stable boundary layer (experimentally observed) with a hydrogen concentration being tens of times higher than that inside the body, the previously obtained hydrogen diffusion equation has been modified. This equation obtained from the first principles and taking into account the influence of the stress-strain state of solid on the transport process of the gas component, was supplemented with a stock term describing the diffusion with trapping modes. This modification was carried out in two ways: using the classical McNabb model and using the tensor of damageability. The boundary-value problem was solved for both approaches. The solution results were compared with published experimental data.