With the advent of nanotechnology, a wide new field of research in various sciences and technologies has been opened for more than two decades. Discovery and production of different nanomaterials and determination of the behavior of matter at nanoscale are among the pillars of this technology. Therein, the realm of nanomechanics is of particular importance since many applications of nanomaterials and nanosystems are dependent on their mechanical properties. In order to expand nanomechanics, the objective of the present dissertation is modeling and simulation of the mechanical behavior of some graphene based nanostructures. Specifically, three subtopics were selected in this regard: (a) Elastic simulation of carbon nanoscroll using molecular structural mechanics approach. In this part, first the geometry of this nanostructure was generated through coding. Then, establishing connection between the chemical properties of atomic bonds on the one hand and the mechanical properties of structural elements on the other hand, the nanostructure was made equivalent to a structural system which was analyzed via finite element method to determine its elastic properties. The effect of geometrical parameters as well as van der Waals forces on the properties was also studied. Young’s modulus of about 1100 GPa and shear modulus of near 500 GPa are among the results of this part. (b) Simulation of loading of carbon nanotube via molecular dynamics method. In this part, in addition to generation of the geometry, codes were developed to identify the interatomic interactions including bonds, angles, dihedrals and impropers. These interactions were defined quantitatively applying a force field. Next, utilizing molecular dynamics technique and through the three ways of applying strain, force or stress, the model was simulated under loading. Elastic constants (the elements of the stiffness tensor), elastic moduli and Poisson’s ratios for single-walled carbon nanotubes having various geometries were derived and compared with the literature. The effect of nonlinearity of the interatomic potentials was investigated as well. (c) Simulation of the elastic behavior of carbon nanocoil through molecular dynamics method. In this part, the geometry of the intended nanostructure which is more complicated than those of the previous two parts due to the existence of pentagonal and heptagonal carbon rings in addition to hexagonal ones, was created with the aid of finite element mesh generator. Then, again using molecular dynamics technique but this time applying a bond order potential function, the model was simulated subject to tension, its spring constant was calculated and the effect of structural parameters was examined. The obtained results for spring constant fall in the range of 4.4-42.4 N/m. These results are in agreement with other theoretical values reported but are higher than experimental values. The reason behind this discrepancy was discussed. Overall, this dissertation presents examples of modeling nanostructures and application of molecular methods to obtain their mechanical properties. Keywords : nanomechanics, molecular structural mechanics, molecular dynamics simulation, finite element method, graphene, carbon nanoscroll, carbon nanotube, carbon nanocoil, elastic properties.