Since surface atoms determines the chemical properties of reactive material, for an elastic material with small size, surface effects can not be ignored because of the very large surface to volume ratio to form. Adding surface effects, buckling and vibration analysis of nano-plates with isotropic properties has been studied in this work. For the buckling loads on the nano-plate to axial and pure shear is considered. Three materials such as graphene, silver and aluminum have been studied. Graphene has extraordinary properties such as nano-scale size, high mechanical stiffness and roughness, high electrical and thermal conductivity, flexibility (ductility) and magnetic property. The unique properties of this material have received a lot of attention from the scientists. The small scale and surface effects were taken into account using the Eringen’s nonlocal elasticity theory and Gurtin- Murdoch’s theory, Respectively. Nonlocal elasticity theory was employed in this study because the results obtained from this theory have been proved to be in good agreement with those obtained from atomic simulations. The effects of surface properties including the surface elasticity, surface residual stress and surface mass density. The governing equations for the isotropic nano-plates buckling and vibration problems were derived using the classic theory of nano-plates. In order to solve the obtained differential equations, the so-called finite difference method was employed. The finite difference method replaces the plate differential equation and the expressions defining the boundary conditions with equivalent differences equations. The solution of the bending problem thus reduces to the simultaneous solution of a set of algebraic equations written for every nodal point within the plate. Problems were solved using a developed computer code in the Matlab software environment, and the effect of various parameters on the buckling and vibration was studied. The Navier’s method has been used to validate results. The effect of non-local parameter, surface effects, different mode, load ratio, aspect ratio, different boundary conditions and Thermal effects on the critical buckling and vibration of nanoplate have been investigated. It has been shown that the finite difference method method is an effective method in terms of both accuracy and rate of convergence for analysis of nanostructures. When the plate is increased, the surface effects on the critical buckling load ratio is bigger. also by increasing the non-local parameter, effects of the surface elasticity modulus and surface residual stress decreases. On the other hand with an increase the buckling mode, the surface effects diminish. Keywords Buckling analysis nano-plates, Vibration analysis nano-plates, Surface effects, Eringen’s nonlocal elasticity theory, Finite difference method