Polymer solutions, containing clay sheets, were electrospun into nanofibers and microfibers that contained clay sheets inside. Controllable removal of polymer by plasma etching from the surface of fibers revealed the arrangement of clay. The shape, flexibility, size distribution and arrangement of clay sheets were observed by transmission and scanning electron microscopy. The clay sheets were partially aligned in big fibers with normal direction of clay sheets perpendicular to fiber axis. Crumpling of clay sheets inside fibers was observed when the fiber diameter was comparable to the lateral size of clay sheets. Single sheets of clay were observed both by catching clay sheets dispersed in water with electrospun nanofiber mats and by the deliberate removal of most of the polymer in the fibers. Thin, flexible gas barrier films, that are reasonably strong, were assembled from clay sheets and polymer nanofibers. Structure of composite films was characterized with scanning electron microscopy. Continuous film of clay sheets were physically attached to the surface of fiber mats. Spincoating film of polymer and clay sheets was reinforced by electrospun fiber scaffold. Certain alignment of clay sheets was observed in the vicinity of fibers.