Abstract: By usingsemi-analytical method, elastic stability of a simply supportedFGM sandwich circular cylindrical shell under torsion loading wasstudied. The inner and outer layers of the shell are comprised ofthe same homogeneous and isotropic material, and the middle layeris made of an isotropic functionally graded material whoseproperties varies continuously in the thickness direction from theinner layer to the outer layer, and keeps continuation in thematerial properties of the interface. Firstly, based on theFlügge thin shell theory, the governing equations for staticbuckling of the structure in terms of displacements wereformulated. Secondly, by introducing the displacements in terms oftrigonometric functions that identically satisfy the boundaryconditions, an eigenvalue problem for linear algebraic equationsincluding the torsion force parameter is obtained. Finally,critical buckling load characterizing the features of instabilityof the structure were obtained by numerical method. The numericalresults show that the buckling load decreases with an increases inthe radius to thickness ratio, and increases with an increase inthe average value of Young's modulus of the FGM middle layer.