Epitaxial single crystal growth of zirconia (ZrO2) and yttria stabilized zirconia (ZrO2 ·Y2O3) films on sapphire substrates was achieved for the first time by using reactive sputtering. And the relations of crystallographic orientations between the epitaxial films and sapphire substrates was determined. Yttria stabilized zirconia films seem to offer hiah quality SOI substrates, since the crystal structure of ZrO2·Y2O3 is cubic fluorite and its lattice constant is closely matched to those of semiconductors such as Si and GaAs.