A buffer (1) for paper cores comprises: a structure (2); a plurality of planes (5), arranged one over the other for accumulating cores; a mechanism (6) for feeding the cores associated with the planes (5) to provide the cores being fed; a first device (11) for transferring cores by the mechanism (6) to one of the planes (5), the first device (11) being interposed between the mechanism (6) and the planes (5) and being movable from one plane (5) to another in order to transfer the cores to the latter; a mechanism (16) associated with the planes (5) in order to discharge the accumulated cores; a second transferring device (21), interposed between the planes (5) and the mechanism (16), for transferring cores from the planes (5) to the mechanism (16), the second device (21) being movable from one plane (5) to another in order to empty the planes (5).