The purpose of this study concerns the establishment of numerical model of transient flow in a variably saturated porous medium. Groundwater flow can only be studied adequately if one considers the fluxes between the saturated and the unsaturated zones through the free surface. However, this water table undergoes variations in level resulting either from losses of mass by gravity drainage or evaporation or from an excess of mass by infiltration from the surface of the porous medium. This describes the various phenomena that groundwater flow can undergo, such as gravity drainage, infiltration and evaporation. The adopted model is based on the Richards equation, which is a parabolic and strongly non-linear equation. The h-based form of the Richards equation is solved numerically by using the 1D upwind finite difference method. Referring to published experimental work and comparing our numerical results with their results, we have obtained a good fit. The importance of this model lies in its simplicity and its generality in treating the different flow states in a variably saturated porous medium, and therefore its usefulness in practice for a wide range of applications, contributing significantly to the understanding of transient flow phenomena in variably saturated porous media. Its capacity to address the complexities of groundwater movement, including gravity-driven drainage, infiltration, and evaporation, underlines its versatility and its potential to make meaningful contributions to various scientific and engineering fields.