In the seismic analysis of saturated porous media, the soil skeleton and the foundation are fully coupled. However, the relative movement of the pore fluid phase to the soil skeleton is governed by the drainage conditions. Consequently, in soil-structure interaction analyses, the stiffness matrix coefficients can be significantly altered in a saturated environment, and impedance functions of a foundation on saturated soil can differ markedly, depending on whether drained or undrained conditions are considered. This study investigates the dynamic impedance functions of a rigid, massless strip footing on homogeneous saturated soil using advanced 2D finite element modeling in Plaxis. The analysis explicitly evaluates the effects of drainage conditions, Poisson’s ratio, permeability, and material damping. The results demonstrate that undrained conditions substantially alter the dynamic stiffness and damping across all impedance components (horizontal, vertical, and rocking). For example, horizontal dynamic stiffness increases by up to 40%, and vertical/rocking components showed significant changes compared to drained conditions. These changes are attributed to the development of excess pore water pressure. Furthermore, the influence of Poisson’s ratio is highly dependent on drainage—it is negligible under undrained conditions, which shows less than 5% variation but significantly enhances horizontal stiffness under drained conditions (up to 30%). Permeability variations most markedly affect horizontal stiffness, with responses converging as permeability decreases toward undrained behaviour. Besides, material damping systematically reduces dynamic stiffness (by 15–20% for ξ = 10%) while increasing energy dissipation, with the horizontal component showing the highest sensitivity. These findings highlight the predominance of the fluid phase in saturated soil-foundation systems, underscoring the importance of accounting for detailed drainage conditions and fluid-solid interactions in accurate seismic design and numerical modeling of foundations in saturated environments.