A new set of acoustical physical constants for ZnO was obtained by ultrasonic microspectroscopy (UMS) using very conductive and resistive (001), (100), and (101)ZnO specimens, grown by the hydrothermal method. The specimens were selected from a lot of small ZnO crystals evaluated with the velocity of leaky surface acoustic waves (LSAWs) on a water-loaded specimen surface, in order to identify proper specimens or proper measurement positions for bulk-wave velocity measurements. The constants were determined with measured bulk-wave velocities, according to the determination procedures developed previously. Their accuracies were estimated by comparing the measured LSAW velocities with the calculated ones using the determined constants, within 3.1 m/s. We observed LSAW velocity distributions and bulk-wave velocity dispersions for some specimens that were related to the resistivity distributions on the specimen surfaces and inside the specimens. We established experiment procedures to apply our UMS technology to ZnO crystals in this study. This ultrasonic method is useful for further understanding ZnO crystal growth processes in the hydrothermal method. This application is extended to other class-6mm crystals.