During the operation of Graphite -fuel HTGR (High-Temperature Gas-cooled Reactor) nuclear reactors, Graphite  used as a neutron moderator, is irradiated and has a variety of contaminants (such as Cs-137, Co-60, and Sr-90) and due to industrial and environmental considerations, decontamination of irradiated Graphite  is very important. In this study, the decontamination of Cs-137 trapped in Graphite  pores of Graphite -fuel (HTGR) nuclear reactors has been analyzed. The proposed method for decontamination of irradiated Graphite  surfaces is the thermal plasma-sputtering method with noble feed gases, which are used to reduce the risk of radioactive Graphite  waste and in this regard, a mathematical model was developed to describe the process of decontamination of irradiated Graphite, which is prone to release Wigner energy due to defects and torsion caused by radiation. The results show that the decrease in radiation pollution of irradiated Graphite  waste and various parameters of its decontamination process depend on the release of Wigner energy. The results obtained are in good agreement with the other researchers results.