A transient mathematical model for a vertical solar still is presented. It is based on an analytical solution of the energy balance equations for the different components of the still. The flowing water temperature is assumed to vary with time and space coordinates. Parametric investigation for the still has been performed by computer simulation on a typical summer day (5th June 1997) in Tanta. It is found that the daily productivity of the still increases with increase of the still length L, width b, and wind speed v up to typical values for these parameters. An optimum area of the still absorber was found to be 3.5 m(2). Moreover, the daily productivity of the still was found to decrease with an increase of the gap spacing between the absorber and the glass cover. The productivity also decreases with increasing the thickness of flowing water d(w). The daily efficiency of the still is about 29%.