The two-continuum rheological model taking account of a change in the hydrogen-binding energy has been proposed in this paper. As in the case of conventional approach our model makes it possible to describe the hydrogen transfer and its accumulation in the metals and to explain changes in the mechanical properties of metals that are caused by that accumulation. The proposed rheological model describes the hydrogen transition from a mobile state to the bound one, depending on the stress-strain state. Concurrent with this achievement, our model describes the changes in the material matrix taking place as a result of the hydrogen addition to the matrix atoms. These processes lead to weakening and destruction of the material.