Carbon nanostructures, including graphene sheets, carbon nanotubes, and fullerenes, are among the most important, most studied, and most promising nanomaterials. Their exceptional mechanical, physical and chemical properties have led to various applications, for which the design process is directly or indirectly dependent on the analysis of mechanical properties and behavior. In this book, a novel simulation method for nonlinear mechanical analysis of carbon nanostructures is introduced. This method is based on the development of the hybrid atomistic-structural element. Nonlinear formulation of this element and numerical solution procedures are discussed in details. This method has been used for studying elastic properties, stability, post-buckling and vibrations of carbon nanostructures.