The flue-wall deformation during the service life of carbon anode baking furnaces has a substantial impact on the carbon anode quality (i.e., thermal, electrical, and mechanical properties) used in the reduction cell of aluminum production. Deformation of the furnace flue-walls, which is one critical mode of furnace aging, leads among others to inhomogeneous baking of the anodes and consequently to a deterioration of the resulting anode quality. This paper focuses on the development of a 3D multi-physics computational model, which is able to take into account a large number of physical phenomena and parameters that play a role in the baking process while considering different levels of the flue-wall deformation. In fact, this 3D model takes into account the thermo-hydro-mechanical coupling due to coupled fluid flow and transient heat transfer, packing coke load and the thermal expansion, and enable us to analyze the influence of these parameters on the resistance to deflection of the flue-walls, and ultimately improved baking process and furnace geometry can be proposed The developed model can predict the anode temperature distribution, creation of hot spot and anode overbaking in certain area as a function of the flue wall deformation mode. By developing this tool, we can effectively predict the deformable flue wall reliability under varying operating conditions, and provide useful insights on enhancing the long-term structural integrity through furnace retrofitting or design adjustment.