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The investigations of changes in bed surface of sediment due to the fluid flow and tracing sediment motion are complex and attractive for the researchers. In the recent decade, modeling of fluid flow using the Lagrangian methods, e.g. Smoothed Particle Hydrodynamics (SPH), is of interest. In this study, the open-source two dimensional SPHyiscs code is used to model the two phase Newtonian and non-Newtonian flows using the μ(I) visco-plastic model, which is obtained according to particle properties including inertia and friction coefficient. First, and in order to study the visco-plastic model, the one phase code is extended to non-Newtonian and the SPH results are compared with the experimental model of the collapsing granular column, where a harmonic interpolation is used for the viscosity of particles. In this stage, the comparison of the SPH model with the experimental data shows a good agreement. Then, the numerical method is utilized for the simulation of Newtonian dam-break fluid flow over a movable bed. The proposed model treat sediments as a non-Newtonian fluid using μ(I) model, by implementing the harmonic interpolation for the viscosity coupled with the Owen’s relation at the interface. Results show that the proposed model has a capability for simulating two-phase water sediment systems.