We determined all the independent components of the acoustical physical constants (elastic constant, piezoelectric constant, dielectric constant, and density) of LiNbO3 and LiTaO3 crystals grown from the melts of three different starting materials with the Li2O contents set to 48.0, 48.5, and 49.0 mol %, and obtained the chemical composition dependences of the constants of each single crystal around the congruent composition. All the constants as well as the measured longitudinal, shear, and leaky surface acoustic wave (LSAW) velocities varied linearly with the composition ratios in the experimental range. The composition dependences of the LSAW velocities for the 128°YX-LiNbO3, X-112°Y-LiTaO3, and 36°YX-LiTaO3 substrates, previously obtained by line-focus-beam acoustic microscopy, were well matched with the calculated ones using the constants determined. Therefore the data of the composition dependences of the determined constants enable us to easily prepare the calibration lines for evaluating the crystals for any arbitrarily cut specimen surfaces, wave propagation directions, and modes by numerical calculations. © 2002 American Institute of Physics.