Results of the strain effect theoretical investigation for YBa2Cu3O7-x thin film based surface acoustic wave (SAW) structures are presented. Third order elastic moduli of YBa2Cu3O7-x polycrystals at room temperature were evaluated and used to calculate the coefficients of SAW phase velocity sensitivity with respect to deformations and rotations both for the YBa2Cu3O7-x polycrystalline substrate and YBa2Cu3O7-xSrTiO3 laminated structures with various crystallographic orientations of SrTiO3 single crystal substrate and YBa2Cu3O7-x polycrystalline film thicknesses. It has been shown that strain effect values in such structures are determined, above all, by the YBa2Cu3O7-x layer thickness rather than by substrate characteristics and substantially exceed all the literature data on other SAW materials and structures.