The background of deep peak-shaving poses demanding requirements for the performance of metal components in thermal power plants. The cracking of the connecting fins on the side wall of the flue seriously endangers the safe operation of the system. Herein, welding simulations were carried out using the finite element method to understand the cracking process of the connecting fins. By changing the welding process and fin size, their effect on stress and deformation was explored. The results showed that increasing the welding rate would decrease the flexural deformation of the flue-side wall. Additionally, the yield range of the connecting fin depended more on width than thickness, and increased with increasing width. As for the relationship between fin size and flexural deformation, the maximum deformation decreased with the increase in thickness, while it first decreased and then increased with increasing width. Overall, the post-welding stress and deformation of the boiler flue side wall exhibited more sensitivity to the fin width compared with the fin thickness and welding rate. This article clarifies the stress distribution status of the connecting fins in the flue side wall under different welding conditions, providing a basis for analyzing its cracking phenomenon, and further providing theoretical guidance for optimizing the structural parameter design of the side wall.