In the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytical approach has been applied to obtain exact results from various boundary conditions. Due to the fact that there is not any research about the buckling of nanoplates based on the S-FSDT including the couple stress effect, the obtained results have been compared with the molecular dynamic simulation and FSDT papers which use the Eringen nonlocal elasticity theory. At the end, the results have been presented by making changes in some parameters such as the aspect ratio, the effect of various non-uniform loads and the length scale parameter.