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This paper presents an investigation of the hydro elastic behavior of vibrating blades in hydraulic machines, which is of strong interest for turbo machinery applications. As a representative case study for vibrating blade in hydraulic machines, a NACA 0009 oscillating hydrofoil is considered. The aim is to model the hydrodynamic moment acting on the oscillating hydrofoil. Two types of oscillation are investigated: forced and free motions. The fluid torque acting on the hydrofoil is modeled introducing an added moment of inertia, a fluid damping and a fluid stiffness coefficient. The model coefficients are identified through an investigation in the frequency domain of the forced motion. The influence of the frequency and the upstream velocity are investigated. The model is then validated in case of the free motion: numerical simulation and model prediction show good agreements in terms of frequency and dimensionless damping.