The discriminant of thin-wall structure thermal buckling instability boundary was derived from governing equations of plates in which the stress function and deflection function are two variables, and the two buckling factors which are local temperature and compressive stress were included in the equations. Then, the gained thermal load and design pressure load were used to capture the dangerous place of combustor liner through static analysis considering thermal buckling instability factors. The critical temperature and critical compressive stress which are required parameters of local thermal buckling discriminant were calculated with finite element method (FEM) and sub-model technique. Finally, a judgment of local thermal buckling was performed through the discriminant. In order to verify the method, the results of certain combustion chamber calculated by the method were compared with the experimental data. It is concluded that the local thermal buckling analysis method is accurate and effective.