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In this paper, we propose a novel transmit/reflect switchable frequency selective surface (FSS) in millimeter wave band based on the effective medium theory under quasi-static limit, which is designed with square-hole elements cut from continuum dielectric plates. The building elements of the surface are composed of all dielectric metamaterial rather than metal material. With proper structural design and parameters tuning, the resonance frequencies can be tuned appropriately. The frequency response of the surface can be switched from that of a reflecting structure to a transmitting one by rotating the surface 90∘, which means under different incident polarizations. The reflective response can be realized due to the effect of electric and magnetic resonances. Theoretical analysis shows that the reflective response arises from impedance mismatching by electric and magnetic resonances. And the transmitting response is the left-handed passband, arises from the coupling of the electric and magnetic resonances. In addition, effective electromagnetic parameters and the dynamic induced field distributions are analyzed to explain the mechanism of the responses. The method can also be used to design switchable all-dielectric FSS with continuum structures in other frequencies.