. With the pervasive development of nanotechnology and the discovery of nanostructures such as graphene, mechanical and thermal behavior of these materials have been widely studied by numerous researchers in the scope of mechanical science. Problems and limitations against experimental investigation of these materials due to their small size and cost-intensive nature of conducting such investigations through atomic simulations has led to the development of modeling approaches to the study of these nanostructures based on mechanics of continuous medium. Modified couple stress theory is among the theories presented by researchers for the investigation of these nanostructures, where small-scale effects are taken into account in the investigation of these materials by introducing higher-order gradients in strain energy. In this thesis, using modified couple stress theory and adopting the proposed displacement field by Shimpi, the mechanical and thermal buckling of graphene nanoplates as well as free vibration analysis of these nanostructures were performed. The required relationships to undertake such an investigation were extracted using conventional finite strip method. Along with these evaluations, parameters affecting the nanoplates and the changes in the behavior of these nanostructures by changing such factors as small-scale effects, effects of nanoplates dimensions, and loading pattern of the nanoplates were investigated. Furthermore, behavior of multilayer graphene nanoplates and effects of van der Waals forces between them were studied and presented. Keywords : graphene nanoplate, modified couple stress theory, two-variable refined plate theory, mechanical stability, thermal stability, free vibration, finite strip method.