In recent studies, nanoindentation experiments combined with the Oliver and Pharr method (OP method) are frequently used to measure the mechanical properties of “one-dimensional” structural materials (micro/nanowires and nanobelts) regardless of the corresponding assumptions of the OP method. This article reports the numerical simulation studies of the nanoindentations of wire structural materials on elastic-plastic substrates using dimensional analysis and the finite element method. We find that the measured hardness and Young’s modulus of wire structural materials are significantly influenced by their geometries and indenters as well as the mechanical properties of substrates and wires.