A novel procedure, based on the Resonant Beam Technique, and its application to anisotropic composites is presented. The evaluation of the elastic modules of anisotropic materials from the measurement of the transverse eigenfrequency spectra of resonant beams is performed by a two step process: firstly the beams cut out from the test material in different directions are evaluated in-dependently of each other under the assumption, that they are isotropic, solving Timoshenko's equations using an isotropic correction factor for shear. Secondly the beams are evaluated together as representatives of one anisotropic material, using an anisotropic correction factor for shear. The equipment, developed for such measurements is presented. Finally, the procedure is applied to a transversely isotropic carbon fibre-reinforced carbon composite and the relevance of the results is discussed.