Displacement instability of the thermally grown oxide (TGO) is a fundamental source of failure in thermal barrier systems. In this work, a finite element analysis has been performed to analyze the displacement instability occurring at a heat resistant metal with superficial TGO subjected to thermal cycling. Lateral and in-plane growth of the TGO which happens during high temperature is simulated by means of material property change from the substrate metal to the TGO. Most of the material properties including the TGO growth are based on the results experimentally obtained in-house. Results of the finite element analyses agree well with the experimental observation, which proves the accuracy and validity of this simulation. The technique will be useful for future work on more complicated phenomena such as deformation under thermo-mechanical cycling.