In the present study, a single cell of SOFC with five layers including two ferrous base metal layers, one YSZ electrolyte layer, one anode layer with Ni/YSZ structure, and one cathode layer of LSM is considered. Physical parameters like how to warm up, mechanical contact, and thermal contact are effective in the thermal-structural analysis of this SOFC and need to be addressed. Zirconium Oxide, because of having the property of the conducting O2- at about 800 °C, which is the operating temperature of the fuel cell, is the basic material for use in the SOFC. Since the solid oxide fuel cell needs to heat up, thermal stresses between these layers are created. The finite Element Method has been applied in this study to study the fracture procedure of a SOFC during warm-up. All parameters seem to play a role in a thermal-structural finite element analysis such as the mechanical contact presence, how to warm up in radiation or isothermal condition, and thermal contact resistance is investigated. While, common simplifications in finite element method, like fields solution independently or simultaneously, and defining material properties as layered elements (composite layer to decrease computation) are also considered. Using ANSYS software to carry out analyses and calculations, finally, a proper model with minimum error and analyzing time is presented.