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We consider a two-degree-of-freedom model where the focus is on analyzing the vibrations of a fixed but flexible structure that is struck repeatedly by a second object. The repetitive impacts due to the second mass are driven by a flowing fluid. Morison’s equation is used to model the effect of the fluid on the properties of the structure. The model is developed based on both linearized and quadratic fluid drag forces, both of which are analyzed analytically and simulated numerically. Conservation of linear momentum and the coefficient of restitution are used to characterize the nature of the impacts between the two masses. A resonance condition of the model is analyzed with a Fourier transform. This model is proposed to explain the nature of ice-induced vibrations, without the need for a model of the ice-failure mechanism. The predictions of the model are compared to ice-induced vibrations data that are available in the open literature and found to be in good agreement. Therefore, the use of a repetitive impact model that does not require modeling the ice-failure mechanism can be used to explain some of the observed behavior of ice-induced vibrations.