A process is described whereby highly ordered arrays of epitaxial thin-film nano- and mesostripes can be grown using molecular beam epitaxy (MBE) techniques on M-plane sapphire alpha-Al2O3 (10 (1) over bar0) substrates. The planar sapphire substrate surface is unstable, and spontaneously forms primarily ((1) over bar 101) and (1 (1) over bar 02) nanofacets upon annealing at a high temperature. By employing this nanofacetted sapphire as a substrate for MBE growth at controlled shallow incident angles, perfect nano- and mesostripes can be produced by means of geometrical shadowing in conjunction with partial de-wetting of the epilayer on the facets. Advantages over other stripe fabrication strategies include: epitaxial quality, tunable width, and the ability to grow superconducting and rare earth nanowires using well-established MBE techniques. The process is demonstrated by the growth of regular arrays of 100 nm wide Nb nanostripes. Additionally, we have determined the epitaxy of Nb (111) on the Al2O3 ((1) over bar 101) facet. The applicability of the periodic defect structure of Nb layers of uniform thickness on the facetted surface is exemplarily demonstrated for the study of the vortex dynamics of type 11 superconductors.