Abstract: An optimized method is put forward for the conventional sigma coordinate system which will cause a dynamical change size of an orifice and have difficulty in the specifying the free surface boundary condition.And 1D flow model is adopt ed to determine the vertical 2D free surface boundary, namely, "movable rigid-lid" used to get the boundary condition.Based on the flow characteristic in front of the bottom orifice and stability analysis of the underwater slope, it introduces the boundary condition of sediment exchange near the riverbed and the expression for the critical condition of riverbed sliding in the initial stages of the bottom orifice outflow respectively.So a vertical 2D flow and sediment mathematical model for bottom orifice outflow is proposed.It is validated by the flume experimental data for the riverbed deformation of scouring funnel shape with rigid apron.Satisfactory agreement is obtained in the length of scouring even segment and the slope of scouring funnel.It shows the rationality and reliability of this proposed model.