Recently, it has been demonstrated that Vibro-Impact Nonlinear Energy Sink (VI-NES) can be used efficiently to mitigate vibration under transient loading. In this paper, the behavior of an harmonically excited Clamped-Free (C-F) beam with an embedded VI-NES is investigated theoretically. Due to the small mass ratio between the beam and the flying mass of the NES, the equation of motion are analyzed using the method of multiple scales. Theoretical prediction are validate by numerical simulation.