A recently developed crystallographic model, edge-to-edge matching, has been used to interpret the crystallographic features of self-assembled DySi2 nanowires on Si substrates. All of the observed orientation relationships (ORs) and interface orientations of the DySi2 on Si(111), (001), and (110) were predicted by one criterion. The calculated results are fully consistent with the previous high-resolution transmission electron microscopy observations. The preference for each OR and interface was discussed in terms of the competition between thermodynamics and kinetic factors. This model can also be used in other epitaxy systems and has strong potential for future nanostructure design.