In the assumption that the volume fraction of ceramic constituents in functionally graded material sobeys the power law distribution and that the material properties are temperature-dependent and graded in thickness direction,the coupled thermo-mechanical buckling of functionally graded elliptical cylindrical shells is investigated in light of the classical Donnell shell theory and Galerkin's principle.Firstly,the buckling governing equations of functionally graded elliptical cylindrical shells and the critical buckling temperature are analytically derived.Then,the temperature-dependent physical properties of the materials are analyzed respectively under uniform,linear and nonlinear ( considering heat conduction effect) temperature rise.Finally,the variation of critical buckling temperature with the eccentricity of section and with the parameters of material components is explored.The results show that,as the temperature-dependent physical properties affect the critical buckling temperature greatly,it should be taken into consideration in the thermal buckling analysis of functionally graded elliptical cylindrical shells,otherwise the critical buckling temperature will be overestimated by 15%; when considering the temperature-dependentmaterial properties,the uniform temperature rise as a simplified form of temperature may lead to an underestimation of the critical buckling temperature of the real structure; and that the critical buckling temperature decreases with the increase of ellipse section s eccentricity,radius-to-thickness ratio and parameters of material components.