It is probable that most molecules in space are formed on the surface of small solid grains in dense molecular clouds. Such grains have generally accumulated icy mantles inside dark clouds. We have investigated the dynamical behavior of a hydrogen atom impinging on the mantle consisting of amorphous water ice based on an MD (Molecular Dynamics) computer simulation to estimate the structure of the resulting grains with the icy mantles. We have found that the hydrogen atoms impinging on the surface of amorphous water ice were easily trapped in a dent of the surface and, consequently they are fixed there firmly. Our results, which neglect tunneling, suggest that the migration of hydrogen atoms over a large region of the surface of icy grains may be less common than is often assumed.