Quantification of seepage through hillsides is important to the understanding of landscape hydrology, run-off generation, erosion processes, and the transport of solutes. For complicated flow domains, numerical solutions have the propensity to be computationally expensive and inaccurate. Analytical solutions are therefore inherently valuable; they also provide a means of checking the accuracy of numerical solutions and, because they provide continuous velocity fields, are extremely useful in generating descriptions of solute transport. This paper presents a method for obtaining analytical solutions for seepage in the saturated zone of homogeneous hillsides with arbitrary surface geometry, using a least squares method to determine the coefficients in a series expansion of the Laplace equation. It determines the (initially unknown) water table location and accommodates arbitrary shapes of the lower impermeable boundary. Flow solutions for a variety of flow domain geometries are provided, with the upper and lower boundaries expressed as cubic splines and piecewise linear polynomials. ¿ American Geophysical Union 1993