The goal of this study is to investigate some crack behaviors which affect the crack propagation angle at the planar solid oxide fuel cell with cracks under the fabricating and operating temperature and analyze the stresses by 3 steps processing on the solid oxide fuel cell. Currently, there are lots of researches of the performance improvement for fuel cells, and also for the more powerful efficiency. However, the planar solid oxide fuel cell has demerits which the electrode materials have much brittle properties and the thermal condition during the operating process. It brings some problems which have lower reliability owing to the deformation and cracks from the thermal expansion differences between the electrolyte, cathode and anode electrodes. Especially the crack in the corner of the electrodes gives rise to the fracture and deterioration of the fuel cells. Thus it is important to evaluate the behavior of the cracks in the solid oxide fuel cell for the performance and safety operation. From the results, we showed the stress distributions from the cathode to the anode and the effects of the edge crack in the electrolyte and the slant crack in the anode. Futhermore the crack propagation angle was expected according to the crack length and slant angle and the variation of the stress intensity factors for the each fracture mode was shown.