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This paper deals with the mechanical buckling analysis of functionally graded material (FGM) sandwich plates using quadrilateral element Q4γs based on the discrete shear projection method (DSPM) to avoid shear locking. The element has four-node and five degrees of freedom per node. It allows modelling two types of FGM sandwich plates, i.e. type A with a homogeneous core and FGM face sheets, and type B with homogeneous top and bottom layers and an FGM core. Different thickness schemes have been considered leading to symmetrical or unsymmetrical geometrical stacking. The paper focuses on the buckling in simply supported square plates under uniaxial or biaxial loads. The linear classical buckling theory (LCBT) is retained to evaluate the critical loads. The results obtained by the Q4γs element are compared with those reported by Zenkour (2005) and using another in-house finite element based on DKMQ and DKQ elements. All results are in good agreement when the LCBT is used to define critical loads, but the paper includes selected non-linear analysis based on the general-purpose finite element software ABAQUS. The results show the limit of validity of the LCBT for unsymmetrical stacking in the sandwich of type A and all sandwich of type B.