The present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is employed and the governing differential equations are obtained using the Hamilton’s principle by considering the Von-Karman’s nonlinear strains. An analytical approach is applied to obtain exact results with different boundary conditions. Due to the fact that there is no research on the stability of micro/nano sandwich plates based on S-FSDT including the couple stress effect, the obtained results are compared with the FSDT studies which use the Eringen nonlocal elasticity.