In this paper mud was treated as the Bingham fluid. In staggered grids, two-dimensional incompressible Navier-Stokes equations for non-Newtonian fluid was solved by the MAC method. Numerical simulations were conducted on mud bed-generating phenomenon and mud impacting a wall along a slope. The distributions of free surface, pressure and velocity of mud and water were obtained. The results indicate that the computed layer thickness of mud bed almost equals the theoretically predicted value. Because of the differences in constitutive relationship, the distributions of free surface are different for water and mud. The distortion of water free surface is much more complicated.