This letter reports on a fully conformal square-patch frequency-selective surface (FSS) consisting of liquid metal alloy embedded within a flexible silicone elastomer. The flexible and elastic nature of the FSS provides high conformity to doubly curved surfaces. The transmission properties of the FSS on both singly and doubly curved surfaces are studied. This FSS can facilitate electromagnetic interference reduction in the X-band frequency range when wrapped on cylindrical or spherical radomes over dipole-like antennas, thus surpassing many existing flexible FSS technologies that usually allow conformable contact only with singly curved surfaces.