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This work presents a switchable frequency-selective rasorber (SFSR) with two operating modes. Switching from transmission to reflection can be achieved by appropriately adding feeders and PIN diodes based on cascaded two-dimensional lossy and lossless frequency-selective surface (FSS) screens. The proposed SFSR can realize out-of-band absorption. Analysis of the equivalent circuit model (ECM) can be useful for achieving a switchable rasorber. As the state of the PIN diodes changes, the working state of the SFSR can be switched from low-frequency reflection and high-frequency transmission to low-frequency transmission and high-frequency reflection, respectively. In the final-revision simulation of the working band of the SFSR, in the ON state, reflection and transmission peaks of -0.55 dB at 4.06 GHz and -0.52 dB at 5.97 GHz, respectively, are achieved; in the OFF state, the transmission and reflection peaks of -0.31 dB at 4.04GHz and -0.26 dB at 6.01 GHz, respectively, are obtained. A prototype sample is developed and validated. The results are in good agreement with those of the full-wave simulation. The proposed design can be used in intelligent anti-jamming communication.