We study the effect of the in-plane epitaxial mismatch between the substrate and the film on the crystallographic structure and the transport properties of YBa 2 Cu 3 O 7−δ superconducting films of thicknesses ranging between 600 and 3000Å. The films are grown by pulsed laser deposition on the new type of single-crystalline substrates prepared by Czochralski method, with the chemical formula (SrAl 0.5 Ta 0.5 O 3 ) 0.7 (CaAl 0.5 Ta 0.5 O 3 ) 0.1 (LaAlO 3 ) 0.2 . We find that superconducting properties of the samples are excellent, and generally they improve with increasing of the film thickness as a result of improved structural ordering. We also investigate the influence of the film thickness on the behavior of the critical current densities.