This thesis presents an atomic-scale study of nanoindentation, with carbon materials and both bcc and fcc metals as test specimens. Classical molecular dynamics (MD) simulations using Newtonian mechanics and many-body potentials, are employed to investigate the elastic-plastic deformation behaviour of the work materials during nanometresized indentations. In a preliminary model, the indenter is represented solely by a non-deformable interface with pyramidal and axisymmetric geometries. An atomistic description of a blunted 90° pyramidal indenter is also used to study deformation of the tip, adhesive tip-substrate interactions and atom transfer, together with damage after adhesive rupture and mechanisms of tip-induced structural transformations and surface nanotopograpghy. To alleviate finite-size effects and to facilitate the simulation of over one million atoms, a parallel MD code using the MPI paradigm has also been developed to run on multiple processor machines. The work materials show a diverse range of deformation behaviour, ranging from purely elastic deformation with graphite, to appreciable plastic deformation with metals. Some qualitative comparisons are made to experiment, but available computer power constrains feasible indentation depths to an order of magnitude smaller than experiment, and over indentation times several orders of magnitude smaller. The simulations give a good description of nanoindentation and support many of the experimental features.