In this study, axisymmetric buckling of annular orthotropic graphene sheet embedded in a Winkler–Pasternak elastic medium is scrutinized for different boundary conditions based on non-local elasticity theory. With the aid of principle of virtual work, the non-local governing equations are derived based on First-order Shear Deformation Theory (FSDT). Differential Quadrature Method (DQM) is also used to solve equilibrium equations. Edges of Nano-plate might be restrained by different combinations of free, simply supported or clamped boundary conditions. To confirm results, comparison of studies is made between results obtained and available solutions in the literature. Finally, a detailed parametric study is conducted to investigate the impact of small scale effects, surrounding elastic medium, boundary conditions and geometrical parameters on critical buckling load. The main goal of this work is to study the effect of various non-local parameters on the buckling load of annular Nano-plate for different boundary conditions, Winkler and shear foundation parameters, annularity and thickness-to-radius ratios. It is seen that for Nano-plates without an elastic foundation, the impact of thickness on buckling load does not depend on values of non-local parameter and annularity. Results also show that impact of elastic basis on the buckling load is independent of small scale effects. Manuscript profile