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The quasi-linear analysis of steady water flow in unsaturated soils involves just two soil parameters, the sorptive number and the (usually saturated) conductivity. The formulation preserves integral capillary flow properties of the soil and yields solutions that are amply accurate for engineering applications. The analog with scattering of plane waves reinforces the utility of the method, making powerful techniques and extant results available from fields such as electromagnetics and acoustics. Solutions for multidimensional infiltration lead to design principles for field permeameters in unsaturated soils. Other applications concern the penetration or non-penetration of unsaturated seepage flows into macropores, cavities, and tunnels. Limited extensions are possible to heterogeneous and anisotropic soils and to unsteady flows.