<p>Coatings bonded to substrates often undergo buckling due to the mismatched interfacial stresses. Understanding the buckling failure mechanism is crucial for optimizing coating structure design and extending its service life. A theoretical model of an elastic coating bonded to a rigid substrate under a mismatched hygrothermal strain is established in this paper, in which the interface between the coating and substrate is described by a linear cohesive zone model. Based on the Föppl-von Kármán hypothesis, the large deformation axisymmetric buckling and post-buckling behaviors of the coating are analyzed with the energy method. Analytical solutions are obtained for the critical hygrothermal strain under three different interface conditions, which are also verified by finite element calculations. Further researches are conducted on the effects of the interface stiffness, critical opening displacement, and aspect ratio of the coating on the critical buckling load. The research results provide a theoretical framework for quantitative prediction and mechanism elucidation of coating buckling failure in real applications.</p>