In view of the design problem of the working amplitude and working frequency of vibrating icebreaking machine, the stiffness and damping value of the ice-snow was identified with the mechanical vibration theory and finite element method. The two-degree-of-freedom mathematical model was established in this paper. And numerical simulation was performed. Then the related icebreaking experiment was carried out. A lot of test and experiment results had proved that experimental data was consistent with the theoretical analysis of mathematical model of vibrating icebreaking system. It was confirmed that the correctness of vibrating icebreaking system's mathematical model and the rationality of its design could be proved.