This paper introduces a new seismic isolation system called a periodic foundation(PF),where inclusions are periodically arranged.The PF is different from traditional base isolation in that it causes a fundamental frequency shift in the structure,thus reducing its response and generating a frequency gap.If the frequency contents of a seismic wave fall into the gap,it can not propagate in the foundation.Thus,it will exert no influence on the structure above.A systematic study of the band of frequency gap for a 2D PF is conducted.The influence of physical and geometrical parameters such as density and elastic modulus as well as filling fraction of the PF and its materials on the band of frequency gap are investigated, and a design with a frequency gap as low as 2.49-3.72 Hz is achieved.This band of frequency gap corresponds well to the design spectra in earthquake engineering.Numerical simulations of a six-story frame structure with different foundations demonstrate that a proposed PF can greatly reduce the seismic response of an isolated structure.This investigation shows that PFs have great potential in future applications of seismic isolation technology. This paper introduces a new seismic isolation system called periodic foundation (PF), where inclusions are periodically arranged. The PF is different from traditional base isolation in that it causes something fundamental frequency shift in the structure, thus reducing its response and generating a frequency gap.If the frequency contents of a seismic wave fall into the gap, it can not propagate in the foundation.Thus, it will exert no influence on the structure. A systematic study of the band of frequency gap for a 2D PF is conducted The influence of physical and geometrical parameters such as density and elastic modulus as well as filling fraction of the PF and its materials on the band of frequency gap are investigated, and a design with a frequency gap as low as 2.49-3.72 Hz is achieved . This band of frequency gap should well to the design spectra in earthquake engineering. Numerical simulations of a six-story frame structure with different foundations demonstrate that a proposed PF can greatly reduce the seismic response of an isolated structure. This investigation shows that PFs have great potential in future applications of seismic isolation technology.