Systems for manufacturing sheets having a highly inorganically filled matrix. Suitable inorganically filled mixtures are prepared by mixing together an organic polymer binder, water, one or more inorganic aggregate materials, fibers, and optional admixtures in the correct proportions in order to form a sheet which has the desired performance criteria. The inorganically filled mixtures are formed into sheets by first extruding the mixtures and the passing the extruded materials between a set of rollers. The rolled sheets are dried in an accelerated manner to form a substantially hardened sheet, such as by heated rollers and/or a drying chamber. The inorganically filled sheets may have properties substantially similar to sheets presently made from traditional materials like paper, cardboard, polystyrene, plastic, or metal. The systems yield sheets can be rolled, pressed, scored, perforated, folded, and glued. They have especial utility in the mass production of containers, particularly food and beverage containers.