The present invention relates to rigid structures and composite materials thereof for providing radiation attenuation/shielding. Some embodiments pertain to a radiation shielding apparatus including: a plurality of positionable radiation-shielding stacks of tiles. The stacks are subsequently and adjacently arranged in a contiguous configuration. A tile positioning mechanism allows movement of tiles within a stack between a stacked (retracted) position and an extended position. In the extended position, the tiles of each of the plurality of radiation shielding stacks at least partially overlap tiles of subsequent and adjacent tile stack at corresponding opposing side-margins thereof.