Abstract: Due to thermal expansion misfit and temperature dependent material parameters among layers of thermal barrier coatings (TBCs), the interfacial stress-strain fields become more complicated under thermal loading, which affecting the TBCs stability and spalling failure directly. In this study, the convex and concave microscopic structure around TBCs interface is simplified as multi-cylinder model, with the classic shakedown theorem, Tresca yield criterion and incremental failure criterion, an analytical method of TBCs shakedown analysis is established, in addition, avoiding the time integral and mathematical programming. The variation between material yield strength and temperature is simplified as bilinear relationship, and the stability of typical TBCs is analyzed by using the method of compensation transformation to simplify the solving process. The results show that the stability limit can be obtained facility by using the analytical model of shakedown analysis based on the cylinder model. Stability limit of TBCs was significantly higher than the elastic limit, and the regional stability limit in convex area is higher than concave area around the interface, which indicates that failure prior to occur in concave area. The larger the radius of curvature of the substrate and the thickness of TBCs, the higher the stability limit, and those analysis results are consistent with the experimental results. The shakedown analysis method of TBCs built in this study has a great significant influence on the further research on stability of TBCs considering the creep.