Epitaxial, textured Ru2Si3 films were grown by the template technique, a special molecular beam epitaxy method, on Si(111) and Si(001). Epitaxial relationships of the films with respect to the substrate were determined by X-ray diffraction. Two competing orientations were found on Si(111), while on Si(001) two different orientations of comparable strength are present. The observed orientations will be discussed and possible lattice matchings will be proposed.