Abstract. A semi-analytical solution of the Richards Equation on a two-layered one-dimensional soil is derived under a constraint that the constitutive relations are exponentially dependent on the pressure head. It allows for a transformation of the equation into a linear parabolic partial differential equation that governs a spatial-temporal function that represents the hydraulic conductivity. The solution is expressed as a linear combination of a set of eigenfunctions derived from a novel Sturm-Liouville problem that reflects the layer system and an auxiliary function that depends only on the spatial variable and the pressure head at the interface. All the relevant coefficients in the representation satisfy a nonlinear differential-algebraic system gathered from imposing the continuity of the pressure head and its flux at the interface. A Newton method of iteration is applied to solve the resulting algebraic system. Several pertinent numerical experiments demonstrating the approach are discussed. This is joint work with Tilsa Aryeni, Department of Mathematics & Statistics, University of Wyoming