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We developed a new method of determining acoustical physical constants (elastic constant, piezoelectric constant, dielectric constant, and density) of piezoelectric materials with high accuracy. This method acquires velocities of leaky surface acoustic waves (LSAWs) excited on the water-loaded specimen surface, measured by line-focus-beam (LFB) acoustic microscopy, and bulk velocities of longitudinal and shear waves, measured with planewave transducers replacing the LFB device in the same system, together with the dielectric constants and density measured independently, for a small number of specimens. For LiNbO/sub 3/ and LiTaO/sub 3/ crystals, we demonstrated that we could accurately determine the constants by choosing proper propagation directions of LSAWs and bulk waves for three principal X-, Y-, and Z-cut specimens and one rotated Y-cut specimen [(104) plate for LiNbO/sub 3/ and (012) plate for LiTaO/sub 3/]. The accuracy is nearly the same as that for the constants determined only from the bulk wave velocities.