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This paper works on the modal analysis of a viscously damped beam (Bemoulli-Euler type) with elastically flexible constraints subject to a moving mass.In the theoretical approach, the equation of motion are discretized via Galerkin method, and then mathematica-software is employed to obtain the free vibration frequency of the system in the numerical method, the results compare with the pertinent literature, showing the reliability of the procedure and method in this paper, and reveal some of new dynamic behaviour of the system.