Abstract: The grouting technology is a very important maintenance method of the blast furnace stack. In China, the grouting process is completed by experience, so the furnace shell is always burnt and the mud material sometimes permeates into hot metal through the furnace lining, leading to accidents. In this paper, a stress calculation model of the furnace lining in the grouting process is set up with ANSYS software based on the finite element method and the theory of elastic mechanics. By using this model, the stress distribution of the furnace lining in the grouting process is calculated under different conditions of grouting pressure, grouting area and grouting location. It is found that the maximum stress in the furnace lining increases along with the increase of grouting pressure, but the stress concentration locates at the same place, and therefore the grouting pressure can be increased under certain conditions. The increase of single-hole grouting quantity causes the stress concentration location of the furnace lining to move towards the hot surface, so the guiding principle of "small quantity and more holes" should be insisted. The probability of lining cracking at the hot surface increases when grouting at the thinnest area of the furnace lining, so grouting at this area should be avoided. An application of the model shows that the simulation results are reasonable and effective.