The presence of a completely saturated soil medium can significantly affect wave propagation through it. The seismic response of a medium is heavily dependent upon its attenuation characteristics and its natural frequency. It has been observed that saturation in a soil medium can cause damping to the waves due to the viscous drag created between fluid and solid phases. The present study aims to investigate the variation in the natural frequency of the medium due to the presence of water. Multiple finite element analyses are conducted on an idealized 2D embankment geometry to capture the combined frequency shift due to topographic irregularity and saturation. The response of the saturated embankment is then compared with a similar model of completely dry medium. An embankment geometry is selected so that the wave propagation in an earth dam, where the presence of water is vital, can be replicated. A geometric irregularity can also cause a change in frequency compared to a flat ground surface due to its interaction with the waves. The dispersive nature of the saturated soil medium and the topographic irregularity combined cause a frequency shift in the embankment. The three-field u-p-w formulation is used to model the saturated medium, and the response at the top of the embankment is observed for multiple dimensions of an embankment. The frequencies getting amplified also change with respect to the medium’s permeability. The permeability is characterized by the term viscous coupling. The viscous coupling makes the medium dispersive, and this causes different frequencies to be amplified in different permeabilities. As the medium becomes less permeable, the range of amplified frequencies is like that of a dry medium, showing a single-phase wave propagation behavior with high viscous coupling.