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The understanding of mudflow—structure interactions and debris—flow structure interactions is of paramount importance for the rational design of technical countermeasures. However, to date, only a limited number of studies have investigated this subject. We propose here a numerical approach to this topic using a 2D vertical numerical model based on the smoothed particle hydrodynamics (SPH) method. First, we will test the capacity of the model to simulate unsteady free-surface flows of water and viscoplastic fluid in comparison to laboratory experiments. Then, we will use it prospectively, based on a series of simulations of Bingham fluid free-surface propagations, to determine the momentum reduction resulting from the presence of a simple obstacle perpendicular to the direction of propagation and to determine the characteristics of stresses applied to this obstacle in terms of peak pressure and evolution over time.