AbstractThe filtering properties of locally resonant periodic foundations (LRPFs) have inspired an innovative research direction toward the mitigation of structural vibrations. To mitigate the structure-borne vibrations from subways, this study proposes an LRPF equipped with a negative stiffness device connecting the resonator and primary structure. The proposed LRPF can exhibit a quasi-static bandgap covering the ultralow frequency range. These frequency components have the properties of strong diffraction and low attenuation, and they contribute the most to incident wave fields impinging on nearby buildings. By considering the flexible support of ground, the tunnel–ground and LRPF–superstructure systems are coupled, and the mitigation performance of the LRPF is evaluated with the consideration of tunnel-LRPF interaction. The findings show that the superstructure responses can be attenuated effectively in the quasi-static bandgap. The peak responses of the LRPF–superstructure system occur not only at its eigenfrequencies but also at coupled resonance frequencies due to the contribution of the soil compliance. This study provides an analytical method to evaluate the effectiveness of the LRPF for mitigating the structure-borne vibrations from subways.