An apparatus for storing and ventilating cheeses has a plurality of shelves for the cheeses supported at their ends by hollow side walls so that the shelves are arranged vertically one above another. The side walls have passages within them for supply and discharge of ventilating air to the spaces above the respective shelves. To achieve a minimal spacing between shelves, while obtaining good air distribution over the cheeses, each said shelf has at least one longitudinal extending duct for conducting ventilating air along the shelf, which duct is connected at one end of the shelf to an air passage in the side wall and has, spaced longitudinally along the shelf, a plurality of openings for the ventilating air located at the underside of the shelf. Preferably each shelf has two such ducts, one for supply and one for discharge of air.