The paper aims to obtain the analytic solutions of distribution of stress in critical interfaces and their change laws. The analytic solutions of distribution of stresses in critical interfaces were obtained based on theories of elastic mechanic, which could take into account the growth of thermally grown oxide (TGO), TGO morphology, CaO-MgO-Al2O3-SiO2 (CMAS) deposition, change of temperature and the misfit of material parameters. The effects of thermal growth of oxide layer and CMAS deposition on the evolution of interface stress in thermal barrier coatings during thermal cycles were researched, and the initiation and propagation of cracks at critical interfaces were predicted from the stress evolution. After TBCs experienced 24 thermal cycles, the stress σv at the valley of top coating (TC)/TGO interface increased from 0 to 301.44 MPa. The stress σp at the peak of TGO/ bond-coat (BC) interface increased from 617 MPa to 1189.89 MPa. When the hCMAS of CMAS deposition increased from 0 to 150 μm, the stress σv increased from 170.26 MPa to 443.37 MPa, and the stress σp was reduced from 1317.83 MPa to 1050.17 MPa. The TGO growth would promote crack initiation and propagation at the valley of TC/TGO and at the peak of TGO/BC interface. The CMAS deposition would further promote crack initiation and propagation at the valley of TC/TGO interface but suppress crack initiation at the peak of TGO/BC interface. The calculated results of the method proposed were observed to mutually agree with the previous research results obtained by finite element method and model test results. It is proved of accuracy to calculate the interface stress with this theoretical method.