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Embankments are usually constructed along rivers as a defense structure against flooding. Overtopping failure can cause devastating and fatal consequences to life and property of surrounding areas. This motivates researchers to study the formation, propagation, and destructive consequences of such hazards in risk analysis of hydraulic engineering. This paper reports a numerical simulation of failure processes in homogeneous embankments due to flow overtopping. The employed numerical approach is based on a double-point two-phase material point method (MPM) considering water−soil interaction and seepage effects. The simulated results are compared to available laboratory experiments in the literature. It was shown that the proposed method can predict the overtopping failure process of embankments with good accuracy. Furthermore, the effects of the cohesion, internal fiction angle, initial porosity, and maximum porosity of soil on the embankment failure are investigated.