A technique for determining the elastic material constants of a concrete test cylinder from longitudinal resonance frequencies is proposed in this paper. The proposed technique permits calculation of both the material constants (E and μ) from one relatively simple measurement. The formulation is based on an accurate three-dimensional vibration analysis of intermediate length cylinders using the Rayleigh-Ritz method. First, the test procedure is described and an illustrative example is given. The accuracy of the method is then verified through tests on steel and aluminum cylinders. Test results from concrete cylinders are then presented. A favorable comparison between the values of the elastic modulus predicted by the proposed technique, the standard ASTM test procedure and direct mechanical measurement is shown.