The aim of the study is to enhance the productivity of solar stills using an unsaturated porous medium initially saturated by salty water and using concentrating reflector. This paper concentrates on the mathematical model for the porous medium and itssolution using a finite volume approach. Previous studies dealt with wick medium with high water content and liquid saturation in the wick medium was not determined. A physical model for the initially saturated porous medium(sand) has been made. The modeltakes into consideration the salt concentration in the solution, surface and internal water diffusions to humid air as well as salt crystallization. The system of transient one dimensional differential equations for liquid, vapor and dry air mass and momentum conservations and energy conservation was developed together with the boundaries and initial conditions. Capillary motion has been considered for gas and liquid solution. A finite volume method was used for discretisation of the differential equations. A fully implicit scheme was used for unsteady term discretisation while the convective terms (liquid solution, vapor and dry air) in the energy equation are handled by an upwind scheme method. The system of equations is solved by direct method (inverse matrix). The coefficients matrix is a function of five dependent variables (liquid saturation, salt solution concentration, gas pressure, temperature and vapor pressure). The nonlinear equations are solved simultaneously by updating the coefficients matrixat one time step until the four variables converge to prescribed tolerances. The numerical code is written in Matlab. Solution of the model is obtained and discussed.