Superconductor flywheel energy storage system (SFESs) is an electro-mechanical battery with high energy storage density, long life, and good environmental affinity. SFESs have been developed for application to a regenerative power of train, the storage of distributed power sources such as solar and wind power, and a power quality improvement. As superconductor bearing is completely passive, it is not necessary to control a system elaborately but accurate analysis in mechanical properties of the HTS bearing is very important for application to SFESs. Stiffness and damping properties are the main index for evaluation the capacity of HTS bearings and make it possible to adjust rotordynamic properties while operating the rotor-bearing system. The superconductor bearing consists of a stator containing single grain YBCO bulks, a ring-type permanent magnet rotor with a strong magnetic field that can reach the bulk surface, and a bearing support for assembly to SFESs frame. In this study, we investigated the stiffness and damping properties of superconductor bearings in 35 kWh SFESs. Finally, we found that 35 kWh superconductor bearing has uniform stiffness properties depend on the various orientations of rotor vibration. We discovered total damping coefficient of superconductor bearing is affected by not only magnetic damping in superconductor bulk but also external damping in bearing support. From the results, it is confirmed that the conducted evaluation can considerably improve energy storage efficiency of the SFESs, and these results can be used for the optimal capacity of superconductor bearings of the SFESs.