Abstract: Floor coverings of composite tiles having a polygonal ground plan and having elastic properties. A recess which is formed of a hollow space in the composite tiles can include a cylindrical support molded on the underside of the tiles. The walls of each composite tile can be stabilized by a supporting component which is connected to the vertical edges of the composite tiles and preferably extends to the lower edge of the tiles. Laying plates which include an arrangement designed to co-operate with the supports of the composite tiles can be used. The laying plates form a laying system which permits the laying of the composite tiles even on difficult substrates and provide for the laid composite tiles to be easily be lifted.