To ensure the safety of disposal facilities for radioactive waste, it is essential to quantitatively evaluate the performance of the waste disposal facilities by using safety assessment models. This paper addresses the development of the safety assessment model for the underground silo of Wolseong Low-and Immediate-Level Waste (LILW) disposal facility in Korea. As the simulated result, the nuclides diffused from the waste were kept inside the silo without the leakage of those while the integrity of the concrete is maintained. After the degradation of concrete, radionuclides migrate in the same direction as the groundwater flow by mainly advection mechanism. The release of radionuclides has a positive linear relationship with a half-life in the range of medium half-life. Additionally, the solidified waste form delays and reduces the migration of radionuclides through the interaction between the nuclides and the solidified medium. Herein, the phenomenon of this delay was implemented with the mass transfer coefficient of the flux node at numerical modeling. The solidification effects, which are delaying and reducing the leakage of nuclides, were maintained the integrity of the nuclides. This effect was decreased by increasing the half-life and the mass transfer coefficient of radionuclides.