Bottom founded offshore structures loaded by level ice can experience ice induced vibrations. The existing mathematical models of this phenomenon are, unfortunately, rather unreliable. The fundamental reason of this unreliability is the mechanism of the ice-induced vibrations which is not well understood and, consequently, does not seem to be properly accounted for in any of the existing models. In this paper a new mechanism is proposed which explains the majority of documented cases of ice induced vibrations. It is claimed that these are variations in the contact area between ice and structure that govern the global ice load, and thereby ice induced vibrations. A numerical model is developed incorporating the main aspects of the proposed mechanism. The numerical model captures general features of the interaction process. As shown by simulation of two experimental cases from literature, the model can predict all regimes of ice induced vibrations of compliant structures. Furthermore, the model reproduces the aperiodic character of ice loading on rigid structures.