The parallel column or stream tube approach appears convenient to simulate large-scale water flow in the vadose zone. A disadvantage is that this purely one-dimensional modeling approach does not consider interaction between columns. For greater lengths or smaller widths of columns, lateral flow between columns might be large enough to render the approach invalid. Guidance is needed to select the dimensions of columns for a particular application and to quantify the associated error. A benchmark two-dimensional analytical solution was derived for the water content resulting from infiltration in a medium composed of two parallel columns with a uniform initial soil pressure head. Vertical and horizontal flow was assumed to be driven by gravitational and capillary forces, respectively, and the Richards equation was linearized by a judicious choice of hydraulic functions. Expressions were also derived for the horizontal flux and the relative error for the total amount of water in the column when applying the stream tube concept. The solutions were applied for three illustrative soil materials. The relative error was larger for the soil with the finer texture, although the lateral flux rapidly diminished away from the interface because of the low soil water diffusivity. Differences in the saturated hydraulic conductivity between columns proved far more important for errors than differences in retention parameters. The error is inversely related to column width. Depending on the contrast in hydraulic properties, column width should be several multiples of column length. The relative error due to column length is mitigated because of normalization with increasing amounts of water. In addition to being a benchmark for the stream tube approach, the solutions may also be useful for independent deterministic simulations and the verification of numerical schemes.