In this paper, a disposal cell for the high level radioactive wastes (HLW) is studied in order to identify and demonstrate the coupled phenomena evolving in HLW repository. In the disposal cell, the overpack and container, which represent important engineering barriers of disposal cell, may be corroded by the eventual arrival of underground water coming from host rock. The corrosion of metallic components induces a degradation of its useful properties including strength, permeability and volumetric expansions, etc. Based on the concept of disposal cell, different materials (i.e. clay, steel and air) are taken into account in numerical simulation. Their mechanical behaviour are characterised by different constitutive models respectively. In order to overcome the eventual numerical difficulties and quantitatively reproduce the closing process of spaces presented in the disposal cell, numerical methods are formulated to descript the long-term corrosion behaviour of steel and the progressive closure of spaces between the geological barrier and different engineering barriers. The numerical results show us that the spaces can be closed with the volumetric expansion created by the steel corrosion and allows us to obtain some quantitative results on the processes developed in the disposal cell with the consideration of the progressive corrosion of metallic components.