[en] Considered are the theoretical principles of the ultrasonic method for measurement of the elastic constants of the disk-shape samples. Described is the measuring device which makes possible the mechanical vibrations of the disks of about 30 mm in diameter to be excited and monitored. By using the samples of the structural steel 45 and tantalum the effect of the conditions of their fastening between the ultrasonic waveguides on the resonance spectrum of their own vibrations has been defined and the values for the Poisson factor, Young's and shear moduli, the bulk modulus and sound velocity estimated. The estimates obtained are in a good agreement with the available data