Elastic properties and residual stresses are critical for the assessment of the reliability of ceramics components. The thin electrolyte layer of anode supported SOFCs is under a state of high compressive residual stress. In the present study, the elastic properties of this layer as well as the residual stress distribution induced in the anode-supported planar SOFC cell were examined by using the resonant ultrasound spectroscopy (RUS). A modal analysis by finite element simulation demonstrated that the RUS has a great potential to determine these mechanical characteristics. The Young's modulus can be determined from the natural frequencies of the layered sample whilst the residual stress can be determined using the sample with a semi-hole. Estimates of the Poisson's ratio are possible. In the experiment, various individual resonant oscillations were successfully identified using the present RUS system. Hence, by comparison of experimental results and simulations, the elastic properties as well as the residual stress were obtained. Although the proposed method is still experimentally challenging, it could be developed to become a powerful tool to simultaneously determine residual stresses and elastic constants of thin-layered systems.