Safe and resistant infrastructure is an essential component of public safety. However, existing structures are vulnerable to damage resulting from excessive ground movement due to seismic activity or underground explosions. The aim of this paper, which is part of an extensive study, is to develop an isolation system based on periodic materials with H-fractal geometry in order to obstruct, absorb or completely modify the pattern of seismic energy before it reaches the foundations of structures. Fractal metamaterial structures have shown promise for increasing the frequency range prohibited for seismic protection. We report the anti-seismic properties of a seismic metamaterial model based on an H-shaped quasi-fractal cell. The fractal design, also known as seismic metamaterials, has an important impact on the band structures of seismic crystals. Using the fractal as a base unit, anti-seismic phononic crystals were developed, and their band-gap characteristics were shown to display unique features due to the increasing wave propagation path and hybridization between local resonances and Bragg scattering. The seismic–mechanical duality is supposed to provide flexible solutions capable of increasing/widening the band-gaps to improve the level of seismic protection.