Flows in unsaturated medium are frequent in the field of civil engineering and more particularly in geotechnics. The study undertaken here tries to solve the unsaturated transient flow equation in porous media using the finite element method. Numerical solution of a finite element discretization is used along with an implicit integration scheme of the time stepping. A functional one that makes it possible to find the distribution of the hydraulic load has been proposed and a calculation program has been developed. The results obtained by this program called TFAP (Transient Flow Analysis Program) are compared to other previous work in the subject. The authors show the importance of this study through two real examples. Liakopoulos conducted several experiments on the water drainage through a vertical column filled with Del Monte sand. One of these experiments was chosen to perform a simulation by the model. The results of the calculation are compared with the experimental data as well.