Abstract: To design a drainage system for a landfill cover or for a leachate collection systems,the engineer had to estimate the maximum saturated depth over the barrier for any proposed configuration.Based on the Dupuit assumption,numerical solution was presented for steady drainage on a sloping impervious barrier with no flow across the up stream boundary.Compared with the results of McEnroe(1993) and Qian(2004),the present method was shown to be rational.Finally the variation of maximum liquid head in layered drainage media was summarized by use of parameter analysis.