Estimating unsaturated soil hydraulic properties to predict water dynamics through a vertical soil profile under the effects of irrigation, drainage and evapotranspiration is imperative for managing soils in the arid regions. The aim of this work was to determine the soil water retention curve and the hydraulic permeability function of a bare soil profile in a Tunisian oasis threatened by salinization. The developed model combines a numerical inversion of the unsaturated flow equation with the BOBYQA optimisation algorithm. The direct model solved the Richards equation using a cell-centred finite difference model. Hydraulic properties were described by van Genuchten-Mualem models. Input data for the inverse problem are the infiltration flow, soil water contents and pressure heads measured during ponded infiltration and internal drainage tests. Numerical simulations of these two tests were performed considering a homogeneous single-layer soil profile but a better fitting between measured and simulated water contents was obtained when the soil profile was divided into five sub-layers. The hysteresis phenomenon was highlighted from the soil water retention and the relative permeability curves corresponding to the ponded infiltration and internal drainage tests.