The virtual mass and damping coefficients of an open and ducted propeller are determined using URANS computations. Time-accurate simulations are carried out for an open propeller forced to harmonic motion in two separate directions, translational x1- and rotational x4- directions. The analysis produces the diagonal coefficients of the virtual mass m11, m44 together with the diagonal damping terms c11, c44. The cross-terms m14, m41 and c14, c41 are also evaluated. A range of advance numbers is considered in the simulations. Several excitation frequencies and amplitudes are applied in order to determine the impact of viscosity on the vibrational coefficients. Oblique flow cases are also considered and the related virtual mass and damping coefficients are analyzed. The computed cases are compared to potential flow simulations and to published semi-empirical results. The average magnitudes of the coefficients correspond quite reasonably to those computed by the CFD method. However, the viscous effects are found to have a certain impact on some coefficients.