This article analyzes the stress–strain behavior of earth dams, considering the varying soil properties, design features, and external factors such as moisture content and applied loads. It focuses on an operating earth dam located in a 9-point seismic zone, using relevant design data, including the structure’s geometry and physical and mechanical characteristics of its materials. The analysis employs the numerical finite element method, which effectively solves coupled problems involving statics, filtration, and deformation. The findings are presented through displacement isolines and graphs of normal, principal (compressive), and maximum shear stresses, followed by a detailed analysis of the results. A comparison between homogeneous (without a concrete transition zone) and inhomogeneous dam models reveals that including the transition zone, considering moisture content, and recognizing structural inhomogeneity significantly influence the calculations. The study demonstrates that the presence of an impervious screen and a concrete transition zone effectively protects the soils of the retaining prism from non-uniform compression and saturation.