Fully coupled steady fluid-solid interaction (FSI) and flutter simulations were conducted on a NASA Rotor 67 transonic experimental fan to demonstrate the capability of application for capturing various aeroelastic phenomena in turbomachinery. The effect of blade deformation on the aerodynamic performance was investigated by steady FSI. Aeroelastic modes were determined using the modal identification technique for the vibration of the cascade. The proposed identification method successfully estimated aeroelastic modes without significant uncertainty. Aeroelastic eigenvalues were localized around the structural modes in vacuum forming the "mode family", and there was negligible change in their frequency. The calculated aerodynamic coupling between the structural modes was small. Based on the reconstructed local unsteady aerodynamic force, the major damping sources in the 1F mode family were determined to be the shock motion and supersonic region near the leading edge. From these results, it was confirmed that the developed FSI method was applicable to the analysis of unsteady characteristics of blades in multimode oscillation.