Extrusion between the side structure and the level ice is one of the most common scenarios encountered by polar ships. It is of great significance for the design and operation of polar ships to explore the mechanism of the extrusion between the level ice and the broadside. A numerical simulation model of the interaction between the level ice and the broadside is established by using the discrete element method in the current study. The rationality of the numerical model is verified based on the results of a model test on the ice loads during the broadside extrusion conducted in an indoor ice tank. The influence of the variation of the angle between the level ice drift direction and the ship's heading on the ice loads during the broadside extrusion is studied and analyzed based on established numerical model of the extrusion between the level ice and the broadside. The mechanism of the broadside extrusion and the distribution law of nonlinear ice loads are discussed. It can provide technical support for predicting ice loads and structural responses in the scenario involving the extrusion between the level ice and the broadside.