Abstract: An earthquake resistant foundation based on the method of longitudinal wave filtration by periodic or quasi-periodic septate waveguides. The generic septate waveguide comprises either a series of cylindrical or annular polymer members or a stratified medium with air-filled cylindrical channels. In all cases, the polymer members are reinforced along their torsional surfaces. As the waveguides are distributed into a specific matrix, they serve as an isolating and damping device which is placed between the source of sound, shock or vibration waves and the object of protection. The elements of the waveguide are the individual septate cylindrical cross sections, which comprise a configuration of polymer, viscous or non-viscous liquid and air constituents bonded to and separated by the rigid end plates. The method postulates that radial displacement be zero at the boundary between the polymer member and the septum. Furthermore, the polymer member should be incompressible, and the septa are rigid.