To obtain confidence in 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. Thus, safety assessment models require uncertainty management as a key part of the confidencebuilding process. In application to the numerical modelling, the global sensitivity analysis is widely employed for dealing with parametric and conceptual uncertainties. In particular, the parametric uncertainty can be effectively reduced by minimizing the uncertainty of critical parameters in the safety assessment model. In this paper, the numerical model of each step disposal facility (Silo, Near surface, and Trench type) at Wolsong Low and Immediate Level Waste (LILW) Disposal Center is designed by using a two-dimensional finite element code (COMSOL Multiphysics). In order to determine the critical parameters for non-adsorbed nuclides such as H-3, C-14, Tc-99, we introduced the variance-based sensitivity analysis methodology of the global sensitivity analysis. In the case of Silo type, the density of waste is highly sensitive to the total leakage quantity of all nuclides. Additionally, the initial nuclide concentration of H-3 was identified as another important parameter of H-3. On the other hands, the mass transport coefficient showed a high contribution in C-14 and Tc-99. In other types of disposal facilities, the leaking properties of H-3 are significantly affected by the amount of infiltration water. However, C-14 and Tc-99 were found to be more sensitive to the density of waste.