The sudden explosion of methane during underground coal mining is a major dilemma. To mitigate its occurrence and reduce the extent of methane diffusion, gas drainage operations are carried out before mining. This paper investigates methane gas flow in a coal block in order to calculate the pressure of gas and its molecule velocity for methane gas drainage operation. A coal piece surrounded by cleats was used for geometrical modeling and numerical simulation. Movements of fluid and gas molecules in a porous medium were successfully simulated. The numerical solution is based on COMSOL Multiphysics software. The validity of the numerical simulation was assessed using an analytical model with satisfactory results.