A scaled boundary finite-element method(SBFEM) is used for determining free surfaces in two-dimensional steady-state seepage problems.Equations of SBFEM for a seepage problem are derived with a transformation from Cartesian coordinates to scaled coordinates.Governing equations are discretized on boundary of computational domain by SBFEM,which reduces spatial dimension by one,and analytical procedure is applied in the reduced direction.As scaled centre is at intersection point of upstream and impermeable straight boundary of the dam bottom,only free surface and its downstream boundaries are discretized.A governing point method is used to control overflow point in the free surface.A 2-D steady seepage with a free surface in a homogeneous dam is analyzed and compared with experimental result.It shows that the method has satisfactory convergence,accuracy and less amount of data preparation.