Apparatus and method for filling under gravity from a hopper (9), a storage device (2) for articles that has the form of a columnar cavity between opposed side walls with a mass flow of mutually parallel rod-shaped articles descending from the hopper, a cavity-filling device (12) that alternates in use between a closed configuration that blocks a downward flow of the said articles through the device and an open configuration that allows flow of the articles through the device, the device being movable in translation, in alternate upward and downward strokes within the cavity, being in the closed configuration on the downward stroke and in the open configuration on the upward stroke.