Abstract: Multilayer systems are widely used in the infrared widow system. Thermal stresses in the thin films are very important to the functions and reliability of the system. In this paper, the strain and stress distributions in an elastic multilayered strip are calculated. The first-order approximation and the zero-order approximation solutions are proposed for the system when the thicknesses of the film layers are much less than the substrate thickness. Specific results are calculated for the elastic thermal stresses in the ZnS-Y₂O₃-SiO₂ infrared window. The results show that the thermal stresses based on the first-order approximation and the zero-order approximation in two film layers have a relative error about 1.54% and 0.09%, respectively. The zero-order approximation solutions can meet the accuracy requirement very well.