Carbon nanotubes (CNTs) are novel materials with special features. Because of their extraordinary electrical, chemical and mechanical properties, CNTs play a significant role in the emerging nanotechnology industry. Receiving increasing attention are other carbon nanotube-based materials, such as carbon nanorings and carbon nanocoils, which were first observed during the preparation of CNTs or carbon nanofibers. In the last two decades, various approaches have been used for the theoretical modeling of CNTs, including computational material, continuum and multiscale methods. The computational material methods of a molecule mainly involve quantum mechanics (QM) and classical mechanics; however, QM cannot be used to calculate large systems. In the present research, classical mechanics, namely, molecular mechanics (MM) and molecular dynamics (MD), are employed to investigate the structural and mechanical properties of carbon nanotube-based materials. First, the geometric structures of carbon nanotube-based materials, including CNTs, carbon nanorings (CNRs) and carbon nanocoils (CNCs), are considered. A single-walled carbon nanotube (SWCNT) is formed by rolling a graphite sheet to make a seamless cylinder; a capped SWCNT is a cylindrical nanotube the two ends of which are capped by fullerene hemispheres; a defect-free CNR is made by bending a SWCNT into a circular ring and connecting its two ends; and a defect-free CNC is formed by rotating a defect-free SWCNT along the surface of a cylinder to create a spring-like coil with an uniform pitch and coil diameter. Following the establishment of the models, their structural stability is examined. MM simulation is employed to identify their minimum energy structures, and in the optimization process the magnitudes of the calculated forces and stresses are gradually reduced until they become smaller than the defined convergence tolerances. The potential energy per atom indicates the level of stability of a type of carbon nanotube-based material. Taking capped SWCNTs with the same chirality and tube diameter as an example, the lower is their average potential energy, the more stable they will be. The structural properties of both armchair and zigzag CNRs are then investigated using MD simulation, and the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field is used to describe the potential energy surface of the structures. Stability is achieved when the ring diameter goes beyond a certain value, which is different for various CNRs. For example, given approximately the same tube diameters, zigzag CNRs have a much greater critical diameter than that of armchair CNRs, as the two types of rings have different structural characteristics. The critical diameters obtained for both types can be used for reference in electronic device applications and academic research into the other properties of these rings. Because buckling severely reduces the performance level of CNRs, their buckling behavior is studied first in order to understand their other properties. A PCNR is subjected to displacement-controlled loading on the carbon atoms on its two symmetrical sides. Such loading is widely applied in atomistic simulations of the buckling behavior of CNTs. MM is used to find the minimum energy structures of the nanorings. The buckling shapes and critical tension displacements of different nanoring structures are presented. When nanorings of different numbers of circles of atoms are subjected to tension, the buckling range increases with the number of circles stretched. It is found that the buckling shapes of nanorings with even numbers of units are symmetrical, whereas those of nanorings with odd numbers of units, in which buckling easily occurs, are unsymmetrical. This investigation paves the way to study the mechanical properties of CNRs. The fracture mechanism is another crucial issue in the mechanics research. MD simulation is performed to investigate the fracture of perfect and defective CNTs, and the simulation results agree well with those reported by studies using different methods. Then, the fracture mechanism of CNRs with a single vacancy defect is studied using the same MD simulation procedure. Various defective models of two different CNRs are investigated, and two different temperatures are considered to examine the effect of temperature on the fracture behavior of the CNRs. The results show that the vacancies in the CNRs are much more insensitive to their fracture than those in straight CNTs. Owing to buckling and stress concentration effects, the defective CNRs are inclined to be brittle at the region near the stretched sides. The structural characteristics of a (5, 5) defect-free CNC are investigated using MM simulation. The critical spring rising angle for a coil formed by an unstable ring is acquired. The mechanical properties of CNCs are derived using MM or MD simulation with fine time steps. In the tension process, one end of the CNC is clamped, and the other is constrained and then stretched. Different numbers of turns and various spring rising angles are considered to investigate their effects on the spring constant. Based on a classic elastic spring formula, the axial Young‟s moduli of CNCs with one pitch are obtained. The simulations show that the CNCs can be loaded in tension to an extremely high elongation, with no plastic deformation detected.