The elastic properties of carbon nanotubes and nanoropes are investigated using an empirical force-constant model. For single and multi-wall nanotubes, the elastic moduli are found to be insensitive to structural details such as helicity, tube radius, and number of layers. The tensile Young's modulus and torsion shear modulus are comparable to that of diamond, while the bulk modulus is smaller. Single-wall nanotubes exhibit ideal elastic properties: high tensile modulus, flexibility, and light weight. The mechanical properties of small single-wall nanotubes have been studied using molecular dynamics simulations, which predicted a Young's modulus several times that of diamond. However, these calculations were limited to small nanotubes. Most nanotubes are either multi-wall or crystalline ropes of single-wall nanotubes. An empirical force-constant model is used to investigate elastic properties. This model successfully calculates the phonon spectrum and elastic properties of graphite. The local structure similarity between graphite and nanotubes allows the same model to be applied to nanotubes. The model can be easily applied to nanotubes of different sizes, helicities, and layers. For single-layer nanotubes, the elastic constants are calculated from the second derivatives of the energy density with respect to various strains. The Young's modulus is defined as the stress/strain ratio when a material is axially strained. The Poisson ratio is determined by minimizing the strain energy with respect to radial compression and axial extension. The elastic moduli of single-wall nanotubes are found to be insensitive to size and helicity. The Young's and shear moduli are comparable to those of diamond and in-plane graphite. Single-wall nanotubes are stiff in both axial and basal directions. For multi-wall nanotubes, the interlayer distance is comparable to that in graphite. The elastic properties are found to be insensitive to the number of layers. The interlayer van de Waals interactions contribute less than 10% to the elastic moduli. The Young's modulus of multi-wall nanotubes is found to be around 1 TPa, which is lower than previous estimates. Crystalline nanoropes composed of single-wall nanotubes are very anisotropic. They are soft in the basal plane and stiff along the axial direction. The cohesive energy of nanoropes is comparable to that of C60 solid. The weak inter-tube interactions allow the nanoropes to be flexible, with individual tubes able to rotate and slide relative to each other. The empirical force-constant model shows that the elastic properties of nanotubes and nanoropes are insensitive to structural details. The calculated Young's modulus (1 TPa) and shear modulus (0.5 TPa) are comparable to those of diamond. Crystalline nanoropes are ideal materials for nanometer-scale engineering due to their high Young's modulus and flexibility.The elastic properties of carbon nanotubes and nanoropes are investigated using an empirical force-constant model. For single and multi-wall nanotubes, the elastic moduli are found to be insensitive to structural details such as helicity, tube radius, and number of layers. The tensile Young's modulus and torsion shear modulus are comparable to that of diamond, while the bulk modulus is smaller. Single-wall nanotubes exhibit ideal elastic properties: high tensile modulus, flexibility, and light weight. The mechanical properties of small single-wall nanotubes have been studied using molecular dynamics simulations, which predicted a Young's modulus several times that of diamond. However, these calculations were limited to small nanotubes. Most nanotubes are either multi-wall or crystalline ropes of single-wall nanotubes. An empirical force-constant model is used to investigate elastic properties. This model successfully calculates the phonon spectrum and elastic properties of graphite. The local structure similarity between graphite and nanotubes allows the same model to be applied to nanotubes. The model can be easily applied to nanotubes of different sizes, helicities, and layers. For single-layer nanotubes, the elastic constants are calculated from the second derivatives of the energy density with respect to various strains. The Young's modulus is defined as the stress/strain ratio when a material is axially strained. The Poisson ratio is determined by minimizing the strain energy with respect to radial compression and axial extension. The elastic moduli of single-wall nanotubes are found to be insensitive to size and helicity. The Young's and shear moduli are comparable to those of diamond and in-plane graphite. Single-wall nanotubes are stiff in both axial and basal directions. For multi-wall nanotubes, the interlayer distance is comparable to that in graphite. The elastic properties are found to be insensitive to the number of layers. The interlayer van de Waals interactions contribute less than 10% to the elastic moduli. The Young's modulus of multi-wall nanotubes is found to be around 1 TPa, which is lower than previous estimates. Crystalline nanoropes composed of single-wall nanotubes are very anisotropic. They are soft in the basal plane and stiff along the axial direction. The cohesive energy of nanoropes is comparable to that of C60 solid. The weak inter-tube interactions allow the nanoropes to be flexible, with individual tubes able to rotate and slide relative to each other. The empirical force-constant model shows that the elastic properties of nanotubes and nanoropes are insensitive to structural details. The calculated Young's modulus (1 TPa) and shear modulus (0.5 TPa) are comparable to those of diamond. Crystalline nanoropes are ideal materials for nanometer-scale engineering due to their high Young's modulus and flexibility.