The Bystrov explicit analytical solution for viscous, low-Reynolds number flow in layers of variable thickness is interpreted as infiltration in a Gardner homogeneous soil obstructed by a subterranean cavity, stone, or other obstacle. Mathematically, the two-dimensional advection–dispersion equation for the Kirchhoff potential is solved by combination of a term responsible for incident unidirectional infiltration, and a term describing a dipole. Superposition results in a separatrix (a cavity or stone contour), outside of which streamlines are deflected from vertical lines, and constant potential (pressure, moisture content) lines demarcating lobe-shaped domains. The physical impedance of the obstacle causes a buildup of moisture near the leading edge and a dry zone near the trailing edge of the obstacle. The criticality conditions of the model were also tested (i.e., that the moisture content in the flow domain is less than porosity but greater than zero).