Calculating mechanical properties of structures at the nanoscale is a problematic task. Different methods exist for performing the calculations but there is always a trade off between speed and accuracy. This work explores a number of different methods for simulating nanostructures. First, it describes a novel extension to an atomistic finite element method to enable it to perform calculations of the piezoelectric properties of nanostructures. The results are then compared with those from molecular mechanics methods. Next it benchmarks various reactive molecular mechanics potentials and electronic structure methods as tools for predicting the tensile strengths and strains at failure of carbon-carbon bonds. The third-order density-functional tight-binding method (DFTB3) and the adaptive intermolecular reactive empirical bond order potential (AIREBO) are shown to offer the best accuracy while still being computationally cheap enough to model nanostructures. Finally, the two most successful methods from the previous section, DFTB3 and AIREBO, are applied to a selection of nanoribbons undergoing uniaxial tensile strain to the point of failure. The importance of the electronic structure to the mechanical properties is examined and a previously unseen relationship between the tensile modulus of armchair nanoribbons and their nanoribbon index is revealed. Additionally, calculations of the tensile properties of experimentally derived nanoribbons are performed that show cove-types nanoribbons to have excellent mechanical properties.