This paper focuses on the mechanisms and limits for the peak ice load values on inclined marine structures, and presents a buckling model, which explains well the phenomena behind the maximum peak ice loads. The study is based on two-dimensional combined finite-discrete element method simulations of the failure process of level ice against a structure. The simulations yield ice load records, which show consecutive peak ice load events. The complexity of the failure process makes the analysis on the mechanical phenomena behind the peak ice load events extremely challenging. The introduced buckling model assumes that the ice sheet breaks into separate ice floes in front of the structure before the maximum peak ice loads occur. The model is demonstrated to be able to quantify the effect of force chains, which have an important role in the ice-structure interaction process.