In this first paper of this series (Rubin and Or, 1993) we developed a stochastic model predicting spatial moments of soil water matric potential &psgr; and saturation S under conditions of unsaturated steady state flow as function of the spatial moments of log saturated hydraulic conductivity Y, capillarity index &agr;, and plant rooting depth Δ. In this study, we investigate the ability of the proposed parallel columns model to reconstruct two-dimensional flow solutions, and apply the model to spatial estimation using the geostatistical formalism. A finite difference numerical scheme was developed to solve the two-dimensional Richards equation in heterogeneous flow domain and obtain detailed images of the spatial distribution of &psgr; and S and their moments. Two-dimensionally-based images representing ''true'' distributions of &psgr; and S in a vertical cross section (x-z plane) of laterally heterogeneous soil were used in a synthetic spatial estimation problem for comparison with the one-dimensionally-based solution and with kriging estimates. The results show that (1) the means of &psgr; and S were practically identical for the one- and two-dimensional solutions; (2) &psgr; variance obtained from the two-dimensional solution was smaller than the one-dimensional, whereas S variance was larger in the two-dimensional case; (3) a smoothing of &psgr; under two-dimensional flow regime resulted in spatial covariance function of a Bessel type, where as two-dimensional spatial covariance of S exhibited a steep decay near its origin denoting spatial discontinuity; (4) the least smoothing of &psgr; was observed near the surface where nearly one-dimensional conditions exist; (5) during transient flow, spatial covariances assume their steady state form quite rapidly; (6) spatial covariances predicted by the parallel columns model provided good estimates at unmeasured locations with conservative confidence regions for &psgr; estimation and less conservative for S estimation; and (7) analytically predicted spatial covariances provide a means for network design. ¿ American Geophysical Union 1993