Viscoelastic materials are widely used in many applications in practice. However, determination of the elastic and damping properties of these materials is quite difficult in the sense that the identified results may contain high degree of uncertainty. The characterization of viscoelastic materials using the Oberst beam method, based on non-contact excitation and response measurements, is revisited in this paper. The effects of signal processing parameters such as frequency resolution in Frequency Response Function (FRF) measurements, as well as the effects of various single-degree-of-freedom modal analysis methods, including circle-fit, half-power and line-fit are investigated first. Then, the modal loss factors, Young's modulus and shear modulus of some sample viscoelastic materials are identified using both the free-layered and sandwiched samples. The results obtained from different tests are compared, discussed and some recommendations are made so as to identify the damping and elastic properties of typical viscoelastic materials with better accuracy. Analyses of a large number of FRF measurements show that the selection of the appropriate signal processing parameters and the use of appropriate modal analysis method can be very significant during the identification of viscoelastic materials. By following the approach presented in this paper, the damping and elastic properties of viscoelastic materials can be identified with better accuracy using either free-layered or sandwiched samples. The material properties obtained by this approach can be used for developing valid structural models and/or for damping optimization purposes.