The SCR catalyst in coal-fired power plant is eroded by the collision of fly ash on the catalyst surface. However the erosion of SCR catalyst by the collision of fly ash has not been fully studied, especially in terms of fluid dynamics. Hence, in the present study, we focus on the gas and solid flows inside the SCR catalyst duct and their consequent effect on the erosion characteristics. For this purpose, computational fluid dynamics is applied to investigate the two-phase flows and to evaluate the erosion rate for different flow and particle injection conditions. Also, the erosion rate and pressure drop of commonly used square shape are compared with equilateral triangle and hexagon shapes. The pressure drop of SCR catalyst is increased when SCR catalyst surface area per unit volume increases. The erosion rate of SCR catalyst is enhanced when the particle velocity, mass flow rate of particle, particle diameter and cell density of SCR catalyst are increased. From the results, the pressure drop and erosion rate at the catalyst surface can be minimized by reducing cell density of SCR catalyst to decrease particle velocity and number of particle impacts.