: In this work, the mechanical stability of nanoplates under thermal loading was studied. Graphene is the two-dimensional (2D) counterpart of graphite with superior properties. High hardness, excellent electrical and thermal conductivity, high mechanical strength, flexibility and unique magnetic properties are among the most important properties of nanometer-sized graphene. These unique properties have attracted a lot of attention in different areas of science. Buckling is one of the most important issues on the mechanical analysis of plates. So, buckling of plates, especially those made of graphene, was studied in this thesis. Thermal buckling is one type of buckling that is caused due to the temperature rise in the parts and it is a major challenge in the construction of new electronic components. Today's electronics is silicone-based, and graphene is a potential alternative for the future electronic devices. Therefore, the phenomenon of thermal buckling has also been considered in this thesis. In order to take the small scale effects into account, Eringen’s non-local elasticity theory was employed to derive the constitutive equations as the results obtained from this theory has been reported to match well with atomic simulation results. Also, two-variable refined plate theory was utilized to derive the governing buckling equation of orthotropic plate. This theory takes the transverse shear effects into account and assumes a parabolic distribution for the transverse shear strains through the plate thickness. Therefore, the results obtained from this theory are more accurate than those obtained from the classical plate theory. The DQ method was then used to solve the governing equations. This method converts the differential equation into a set of algebraic equations within the problem domain. The main advantage of DQ method over the analytical method is its ability to consider any arbitrary quadrilateral geometry and various boundary conditions. Buckling of arbitrary straight-sided quadrilateral plates with both simply-supported and clamped boundary conditions was investigated. The boundary conditions were imposed using the Shu’s direct method. For the sake of convenience and generality, the governing equations were non-dimensionalized. A computer program was coded in MATLAB software and it was used to study the effect of various parameters on the buckling load. As for the verification purposes, the numerical solution was compared with the Navier’s solution (exact solution) and excellent agreement was observed. The effect of small scale factor for different modes and geometrical parameters that influence the thermal load was also studied. The effect of geometrical parameters, including the aspect ratio of trapezoid, angle of parallelogram and aspect ratio of rectangle, on the buckling load were plotted for different scale coefficients. It was observed that the DQ method is an effective method in terms of both accuracy and rate of convergence for analysis of nanostructures. Moreover, it was found that the critical load ratio is equal to the critical temperature ratio in similar situations. It was also proven that the dimensionless buckling load is independent of the elasticity modulus for isotropic material, and it is dependent on the orthotropic ratio (E2/E1) for orthotropic materials, not on the moduli. Keywords: Thermal buckling, Orthotropic nanoplate, Nonlocal theory, Differential quadrature method, Two variable refined plate theory