The small scale effect on the elastic buckling and vibration of triangular orthotropic single-layered graphene sheets is studied employing nonlocal continuum mechanics. Superior mechanical, chemical and electrical properties of nanostructures cause their wide usage in different nano-devices such as nano-sensors, nano-actuators and nano-composites .Due to their discrete structure, atomistic methods such as molecular dynamic simulations, density functional theory are more proper for the accurate mechanical analysis of nanostructures. As controlled experiments in nano scale are difficult and molecular dynamic simulations are computationally expensive, theoretical modeling of nanostructures would be an important issue as long as the approximate analysis of nanostructures is concerned. AlthoughAlthough classical continuum elasticity is a scale-free theory and cannot foretell the size effects, however, continuum modeling of nanostructures has gained ever-broaden attention.Using local theory for the small size analysis leads to the over predicting results. To predict micro/nano structures correctly, it is necessary to consider the small-scale effects. Some size-dependent continuum theories that take small-scale effects into consideration are couple stress elasticity theory, strain gradient theory, and modified couple stress theory. However, the nonlocal elasticity theory initiated by Eringen is the most common continuum theory used for analyzing the small-scale structures. In order to capture the small scale effects in nonlocal continuum theory it is assumed that the stress at a point depends on the strain at all points in the domain. This is contray to the classical continuum theory in which it is assumed that the stress at a point is just a function of the strain at that point. So, dimensions of a system reduce to the small scale, they become comparable to the inter-atomic or inter-molecular spacing of the system, and so, the material can no longer be modeled as a continuum. In addition, at small scale, the influence of long-range inter-atomic and inter-molecular cohesive forces on the static and dynamic responses of nanostructures tends to be significant and cannot be neglected. In this present work the principle of virtual work is emploied to derive the govering equation. The Galerkin method in conjuction with the area coordinates of the nanoplate is used as a basis for the analysis. The straight- sided triangular domain is mapped into a right angled triangle domain in the computational space using a three-nod element. The solution procedure views the entire triangular nano plate as a single super-continuum element. Nonlocal theories are emploied to bring out the effect of the nonlocal parameter on natural frequencies and buckling parameter of the nanoplates. Effects of nonlocal parameter, lengths of nano plate, aspect ratio, mode number, material properties and different boundary condition on the nano plate buckling loads and natural frequency are investigated. It is shown that the buckling loads and natural frequency depend on the non-locality of the micro/nano plate, especially at the small dimensions and clamped boundary condition. kewords: Vibration and Buckling; Galerkin method; different boundary condition.