Numerical simulation of flow through multidimensional heterogeneous soils under unsaturated conditions is a computationally intensive task. The governing unsaturated flow equation is nonlinear. The degree of nonlinearity depends on the unsaturated hydraulic properties of the soil and the degree of heterogeneity. In this paper, we present a highly efficient method to simulate unsaturated steady state flow through random porous media. Our method utilizes the analytical (approximate) solution derived by a perturbation-spectral method as an initial guess solution for a numerical model to simulate two-dimensional vertical infiltration problems. It is found that this approach, which we call ''ASIGN-ing,'' reduces the required CPU time by one to two orders of magnitude. ASIGNing is demonstrated to operate successfully under a wide variety of boundary conditions which may substantially deviate from those imposed on the initial guess solution. A large range of mean and variances in the independent variables ln Ks and &agr; or alternatively ln &agr; has been tested and it is shown that the method works well for variances of the unsaturated hydraulic conductivity &sgr;lnK'2≤5 and average ⟨&agr;⟩≤0.1 -1>. ¿ American Geophysical Union 1993