In this work, for ZnO single crystals, analytical expressions are obtained for the components of the displacement vector of surface acoustic waves (SAW) generated by a single electrode and an interdigital transducer. The dependences of the SAW amplitudes, as well as the change in phase-matching frequencies in ZnO single crystals, depending on the thickness of the metallization layer, are found. The numerical values of such corrections can reach 30 and 20 percent, respectively.