A simple and noncomputational intensive method is proposed for elastically characterizing an isotropic material. The Poisson’s ratio and the shear modulus are determined from the axisymmetric vibrations of a cylinder with a length equal to its diameter. These vibrations are excited by means of a wide spectrum impact. The optical system used allows the simultaneous detection of several vibration modes. The out-of-plane displacement is detected by speckle interferometry. From the resulting vibration displacement spectrum, the two lowest frequencies are obtained, both corresponding to axisymmetric modes—specifically, the first symmetric mode and the first antisymmetric mode. The values of both dynamic elastic constants are obtained by comparing previously computed nondimensional natural frequencies and the measured frequencies. The method requires only one experiment and needs no electronic computation. The results obtained for an aluminum cylinder are coherent and confirm the appropriateness of the method. The relative difference between the Young’s modulus values calculated by the proposed method and applying the elementary theory to a long rod of the same material is 0.27%. Comparing the shear modulus value obtained by this method and the calculated one from the lower frequency in torsion, a relative difference of 4.6% is found.