This paper presents a numerical analysis to investigate the effect of the vertical flat plate external reflector on the distillate productivity of the tilted wick solar still. We propose a geometrical method to calculate the solar radiation reflected by the external reflector and absorbed on the evaporating wick, and also performed numerical analysis of heat and mass transfer in the still to predict the distillate productivity on four days (spring and autumn equinox and summer and winter solstice days) at 30 degrees N latitude. We found that the external reflector can increase the distillate productivity in all but the summer seasons, and the increase in the daily amount of distillate averaged over the four days is predicted to be about 9%.