The safety of critical infrastructures such as nuclear power plants during an earthquake is a critical issue. The application of engineered periodic media to regulate seismic waves provides an entirely new solution to seismic engineering. In the present study, we examine the effect of periodically repeating unit cells on the damping of vertical propagating shear waves. We employ the matrix formalism to investigate wave transmission through periodic media. Our approach integrates optimization techniques to determine the optimal number of unit cells and, its dimension, and the material properties of the medium with the objective of achieving substantial attenuation across all waves within the frequency range of 1–10 Hz. Findings from this study contribute to the understanding of seismic wave propagation through periodic media and offer deeper insights into the design parameters essential for effective seismic wave attenuation in this frequency band.