PMN-PT, a piezoelectric single crystal, has many useful applications such as sensors and actuators. In this paper, all the elastic, piezoelectric, and dielectric constants of the PMN-32％PT single crystals were measured by the resonance method. For the rhombohedral symmetry, a total of twelve independent material constants were measured such as six elastic compliance constants at constant electric field, two dielectric constants at constant stress, and four piezoelectric constants d. Seven sets of crystal samples of each different geometry were prepared for the measurement of length-thickness extensional, thickness extensional, radial, length extensional and thickness shear modes of vibration, respectively. In order to check the validity of the measurement, experimental impedance spectrum of the PMN-PT crystal was compared with numerical data spectrum calculated with the measured material constants. The good agreement between the two spectra confirmed validity of the results in this paper.