Upon completion, the National Radioactive Waste Repository in Bátaapáti will provide safe storage for low- and medium-level radioactive waste. The emplacement chambers were excavated in a fractured, blocky, granitic rock mass approximately 240 m below surface. One of the tasks related to the repository development is the feasibility demonstration of the permanent repository closure, including long-term rock mass associated issues. The required lifetime exceeds the usual one of an engineering structure. The long-term behavior of the repository needs to be extrapolated from observation over a shorter time period, or from analogous natural caverns. Numerical methods are the most promising techniques to carry out the extrapolation. It is commonly understood that there are significant uncertainties in long-term predictions. Uncertainties can be mitigated by utilizing independent methods to assess long-term behavior and by improving the prediction capability of the calculation model in the short term. The aim of the paper is to: (1) create a numerical model to effectively capture a wide range of the observed behavior of the rock mass, including tunnel-excavation-induced stress change and stress-dependent permeability and (2) identify the possible cause of long-term creep and show that the long-term creep can be captured by the selected calculation method. The moderately fractured rock mass is modeled using the Universal Distinct Element Code, released by Itasca. The joints in the rock mass are explicitly modeled; the blocky nature of the rock mass is captured. The model is verified with actual field observations and monitoring results. Based on the predicted stress state of the rock mass, the potential cause of long-term creep is identified. By fulfilling the two aims explained above, it is concluded that the model can be used to extrapolate in time and serve as a possible estimation method for the long-term behavior of the repository.