The first paper in the series presents the numerical model for saturated-unsaturated water movement in response to hydrological and meteorological processes. The cut-off walls of closed type and semi-closed type are taken as the main objects to be studied. With the main dyke in lower and middle Yangtze as background, the typical double-layer and multi-layer foundation stratifications, dyke section form, and the hydraulic parameters for the saturated and unsaturated zones are given. The hydrological and meteorological processes are provided according to observed data. The way to deal with the boundary conditions of rainfall infiltration and evaporation is presented. The methods to initiate the water movement for models are suggested. It is suggested to analyze the effects of the cut-off on ground water regime through comparing the 2D numerical simulated results with and without cut-off wall. The 3D numerical simulated results are suggested for analying the effects of the flow around the lateral ends of cut-off on ground water regime. The models and parameters possess typicality. The methods are reasonable and efficient.