Gas leakage through the cracks and tracks surrounding Underground Coal Gasification (UCG) is of criteria affecting the feasibility of economic methods of the UCG reactor. In terms of process control and groundwater contamination capacity, the sealing of the UCG reactor is very important. Various factors affect the gas leakage from the UCG reactor. In this paper, the parameters of pressure, temperature and joint characteristics (including opening, length and intensity) as the most important factors affecting gas leakage through rock mass fractures are examined using numerical modeling. For this purpose, The Mazino Tabas coal area is studied as a case study. The DFN-FRAC3D computer program is used to stochastically simulate joints and create an equivalent pipe network. Also, Water Gems software is used for flow analysis. The results are shown that increasing the reactor pressure and increasing the rock mass jointing around the reactor increases the flow rate and the gas leakage. On the other hand, increasing the reactor temperature does not have a significant effect on the output flow rate. Besides, jointing is the most effective factor in fluid leakage through the UCG reactor. Among the geometrical features of the joint, including the intensity, the opening and the length of the joint, the joint intensity factor has been introduced as the most important factor.