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Numerical and computer modeling of various physical processes is a modern trend and is a promising way to solve the problem of determining the magnitude of ice impacts on shelf structures and technical facilities in the Arctic. This paper contains a review and analysis of some numerical methods, which have found their application in modeling the ice–structure interaction process. Such methods as the finite element method (FEM), the extended FEM (XFEM), the Galerkin discontinuous method, the smoothed hydrodynamic particle method (SPH), the discrete element method (DEM), the material point method (MPM), and the new promising smoothed particle Galerkin method (SPG) are considered. The advantages and disadvantages of these methods are presented, as well as the results of various researchers' studies showing the approaches applied to ice fracture modeling in numerical methods under consideration. The paper concludes with an assessment of the most frequently used methods and approaches (FEM and DEM) and recommendations on the use of the SPG method for the task of ice–structure interaction modeling are provided. [ABSTRACT FROM AUTHOR]