In this paper a Nth order nanoplate model is developed for the bending and buckling analysis of a graphene nanoplate based on a modified couple stress theory. The strain energy, external work and buckling equations are solved. Also using Hamilton’ principle, main and auxiliary equations of nano plate are obtained. The bending rates and dimensionless bending values under uniform surface traction and sinusoidal load, the dimensionless critical force under a uniaxial surface force in x direction are all obtained for various plate\\\'s dimensional ratios and material length scale to thickness ratios. The governing equations are numerically solved. The effect of material length scale, length, width and thickness of the nanoplate on the bending and buckling ratios are investigated and the results are presented and discussed in details.

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