Water infiltration and recharge cause stresses, deformations, and displacements in the soil, which can lead to landslides, subsidence, erosion, etc. The objective was to propose a solution for the internal energy equation, (water flow in the soil mass) based on modern mechanics and underground hydraulics. From continuum mechanics, the internal energy equation was analyzed: i) the distribution of water flow at the surface as a source; ii) the expansion of water flow within the soil mass in cylindrical coordinates; iii) the distribution at the upper boundary, and the transient conduction of internal radial flow. Analogous near-surface and internal conduction were proposed as a load source. Stresses, deformations, displacements, and potentials were reviewed using modern mechanics, and the superposition principle was applied. The formulation was applied to a case study. It was found that Cartesian equations best represent the external surface flow of water (runoff), while cylindrical and radial equations best fit the internal flow in the soil (conduction-distribution). The proposed solution is in terms of the supplied load (precipitation). At different soil moisture contents—dry, saturated, and supersaturated—dynamic processes generate different energy rates. Externally, in supersaturated soils, the energy is purely hydraulic and is a parallel mobilization force on the surface (runoff or flooding). This solution could be applied to other multidisciplinary problems in mechanics, geomechanics, and hydrogeology, given the rigor of mathematical formulations that have described problems independently.