The aim of this presentation is to show the ability of STAR-CCM+ to simulate unsteady aerodynamics, using both moving mesh and moving reference frame, in order to evaluate damping derivatives of the NACA 0012 airfoil. The simulations have been performed with STAR-CCM+ for 2D, unsteady, turbulent flow field and animating motions using a JAVA-macro written ad-hoc. The unsteady forces and moments acting on the airfoil have been directly compared with the exact theory of Theodorsen. The match between CFD end analytical data is very good. This lays the right foundation to calculate damping derivatives of the NACA 0012 airfoil with reliability. A series of maneuvers have been performed: pure plunging , pure pitching and flapping maneuver. The flapping maneuver has been performed in two ways: 1) simultaneous combination of pure plunging and pure pitching motion; 2) at first, pure plunge and pure pitch have been performed separately, and then acting forces and moment have been summed together. Given the linearity of phenomena the two previous methods are equivalent. Despite the complexity related to an animated airfoil, turbulent flow field and moving mesh, STAR-CCM+ has shown a great capability to predict the linearity of the phenomena and is in very good agreement with theoretical data.