Cylindrical specimens made of the Ni-based super-alloy Inconel 625 (IN 625) were coated with (a) NiCoCrAlY, or (b) NiCoCrAlY and yttria-stabilised zirconia (YSZ: in this case, zirconia with 7-8 wt% yttria), using the electron beam - physical vapor deposition (EB-PVD) technique. In the bi-layer coatings, the YSZ layer is the thermal barrier coating (TBC) and the NiCoCrAlY layer is the metallic bond coat (BC). The BC improves the bonding between the substrate and the ceramic TBC, while the low thermal conductivity of the TBC offers high-temperature protection to the substrate. This paper focuses on the determination of the elastic moduli of the substrate and the coating layers of the test samples. The elastic moduli of the three different materials (IN 625, NiCoCrAlY and YSZ) were determined by means of a mixed numerical - experimental technique (MNET). The employed MNET was based on the comparison of the experimentally measured resonant frequencies of the first bending mode of the test samples to the numerically calculated ones. The unknown elastic properties were determined by fine-tuning the elastic material parameters of the numerical models so as to enable the reproduction of the experimentally measured resonant frequencies.