Since the discovery of C 60 Buckminsterfullerene (buckyball) in 1985, various architectural types (allotropes) of carbon structures such as single multi-walled nanotubes (SWCNTs MWCNTs), nanorodes, nanorings, monolayer and multilayer graphene sheets are built. One of the latest discoveries, single layered graphene sheet (SLGS), is a single free standing atomic layer of carbon which was first explored by P.R. Wallace in 1947 theoretically, but A. Geim and his coworkers succeeded to isolate this wonder material after 57 years by using micromechanical cleavage method. Nanostructures have shown different properties from their macro scale counterparts such as mechanical strength, electrical thermal conductivity, chemical reactivity, traarency and magnetism. Because of mentioned properties these structures are used in a wide range of applications from electronics (ultrafast transistors, faster processing speed) to medicine (new vehicles for delivery, targeted delivery) to energy (higher energy storage capacity, longer life, a safer alternative) to nanodevices (nanorobots, nanomachines, nanosensors, nanoelectromechanical devices, nanoactuators) and more. In the present paper, the elastic buckling and vibration characteristics of isotropic and orthotropic nanoplates are discussed. The geometry of nanoplates is assumed as rectangular, parallelogram, trapezoidal, triangular, circular, elliptical, annual and sectorial. In order to consider small scale effect, Eringen’s nonlocal continuum elasticity is employed. The governing nanoplate equations are derived by the principle of virtual work. B3-spline finite strip method is applied to the buckling and vibration analysis which is based on the consept of separation of variables. The buckling load and vibration frequency of graphene sheets including different sizes, nonlocal parameters, aspect ratios and boundary conditions under biaxial compression and pure shear loading are investigated. The interaction curve for biaxial compression loading is obtained, as well as the interaction curve between uniaxial compression and shear loading. It is observed that by increasing the nonlocal parameter the effect of small scale becomes important. It is ssen that small scale effect increases when the size of nano plate decreases. Also clamped boundary conditions are affected by nonlocal effect incomparison with simply supported and free conditions. Higher modes of free vibration and buckling are affected by small scale effect. It is seem increasing the aspect ratio of nanoplates induces to vanish the effect of nonlocality. For the first endevior buckling of nanoplates under pure shear loading is studied. It is seen that shear loading is sensitive to small scale effect in comparison with compression loading. It is seen that interaction curves are affected with small scale significantly for plates with smaller sizes and greater values of the nonlocal parameters. It is proved that small scale effect plays considerable rule in analysis of plates at very small sizes. Key words: nanoplate, buckling, vibration, nonlocal elasticity, spline finite strip. ده