The Young's modulus, the shear modulus, the Poisson ratio and the internal friction of typical electrolyte materials for SOFC, (Gd2O3)0.05(CeO2)0.9, (Sm2O3)0.05(CeO2)0.9, (Y2O3)0.08(ZrO2)0.92, (Y2O3)0.1(ZrO2)0.9, (Sc2O3)0.1(ZrO2)0.9, (Sc2O3)0.9Ce0.01(ZrO2)0.89 were evaluated by a resonance method. The measurements were carried out from room temperature to 1273 K in flowing pure Ar. The Young's modulus of (Gd2O3)0.05(CeO2)0.9 and (Sm2O3)0.05(CeO2)0.9 gradually decreased with increasing temperature as expected for the typical ceramics. However, the Young's modulus of the series of zirconia drastically decreased in the temperature range between 573 K and 873 K, and correspondingly the internal friction increased. Such a characteristic temperature dependence of the mechanical properties was discussed in terms of phase change.