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Abstract Groundwater in the unpressurized aquifer is divided into saturated and unsaturated zones, which are separated by the water table. Calculating the groundwater flow in the saturation zone is performed by solving the Laplace equation. Whereas the movement of groundwater in an unsaturated zone requires solving Richards’ equation. The difficulty in calculating groundwater flows is not only due to the high nonlinearity of the Richards’ equation. The problem is even more difficult because the two equations Richards and Laplace have completely different mathematical natures. In addition, in the area near the water table, the two states of saturation and unsaturation alternately change. In this paper, an algorithm for solving one-dimensional Richards’ equations by the finite volume method is introduced. The algorithm allows the calculation of the distribution of moisture in the unsaturated zone and accurate determination of the position of the water table in the interaction with the saturated zone