This paper investigates the buckling behavior of double-layered graphene sheets (GSs) with vaious boundary conditions. It is assumed that two graphene sheets are bonded by an internal elastic medium and surrounded by external elastic fundation. Governing equations are derived based on new first-order sher deformation theory (NFSDT), while the expressions for the buckling load are given in explicit form for a graphene sheets with all edges simply supported (SSSS) and all edges clamped (CCCC). The equations of equilibrium of the nonlocal model have been derived by using the vertical displacement method. Two characteristic types of buckling are considered (in-phase buckling and out-of-phase buckling). The influence of small scale coefficient, aspect ratio, stiffness of internal elastic medium and external elastic fundation on the nonlocal buckling load is explained. Keywords: Analytical modelling, Buckling, Nano-structures
