Equipment for continuously feeding boxes or containers stacked in a flat tubular configuration to a packaging machine which also operates continuously, the equipment being of the type comprising a magazine (M) containing the stacked containers (A), the store being downwardly open and located in the initial part of the cellular conveyor (T) of the packaging machine, and comprising a carousel device for collecting the containers, one at a time, from the base of the store and for inserting them into the cells of the conveyor at the correct time, preferably by means of interaction with opening means for inserting the container in an open condition into the corresponding cell. The magazine is positioned with its lower end at a level which may be slightly above that of the conveyor and suitably upstream thereof, in that a carousel (1) device, rotating about a horizontal axis orthogonal to the direction (F) of continuous advance of the upper run of the cellular conveyor of the packaging machine, is located under the magazine and upstream of the conveyor, in that this carousel device comprises a plurality of suction cup (116) units which are spaced at equal angular intervals from each other and are positioned in a way which is determined by interaction with cams, and in that the units are designed to grip the container and draw it from the base of the store (the first zero reference point) by gripping the base wall by means of which these units subsequently deposit the container in a dynamic way on to the base (the second zero reference point) of the cell of the conveyor, the whole being arranged in such a way as to simplify the adaptation of the equipment to changes in the format of the containers.