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This paper presents a 3D band-absorptive frequency selective rasorber (FSR). Such an FSR is absorptive within a specific band and almost transparent below the absorption band. The definition and evaluation of the band-absorptive FSR is initially provided and followed by the design concept of 3D FSR. An example is then proposed, whose unit cell is composed of 3D absorber and 3D band-stop FSS. An equivalent circuit model is established for understanding its operating principle. A prototype of the proposed 3D band-absorptive FSR is fabricated. The measured results show that it has an absorption band (|S 11 | ≤ −10 dB and |S 21 | ≤ −10 dB) from 4.21 to 6.51 GHz, with a thickness of 0.17 wavelength at 4.21 GHz. Moreover, |S 21 | is higher than −1 dB at the frequencies below 1.28 GHz. The proposed bandabsorptive FSR can be used as radomes for low-frequency antennas in military communications or spectrum monitoring systems. INDEX TERMS Frequency selective rasorber (FSR), absorptive frequency selective structure, bandabsorptive.