Abstract A study is presented on the seepage occurring through homogeneous soil beneath a concrete dam with a downstream filter and taking into account the existence of a lower horizontal impervious sublayer. The problem is hydrodynamically solved by using the Schwartz-Christoffel transformation and a seepage formula is presented. A study on a non-dimensional graphical representation of the seepage formula led to the prediction of the recommended lengths of downstream filters. In addition, the author presents a formula for evaluating the uplift pressure distribution on the base of the dam. Examination of the pressure distribution formula shows that two important boundary conditions are satisfied.