An apparatus (1) is intended for the storage and transport of an elongate endless tape (2). For this purpose the apparatus comprises a storage bin (3) in which at least a part of the tape is stored as a package of tape loops (2a). The bin (3) comprises main walls (4), an entrance wall (5) and an exit wall (9), the walls (5, 9) being formed with an entrance slot (6) and an exit slot (10) respectively, and outlet openings of first and second pneumatic means (15, 20) being provided near both slots to assist in the feed-in and feed-out of the tape. The main walls (4) of the bin (3) are disposed vertically or substantially vertically, the entrance slot (6) being situated near the upper side and the exit slot (9) near the lower side of the bin. At least one of the main walls (4) of the bin comprises discharge means (16) allowing fluid to escape from the bin, which discharge means (16) are spaced from the entrance wall (5) and from the exit wall (9). Near the bottom of the bin wall portions of the exit wall (9) extend in a V-shape towards the exit slot (10) and at their upper sides they are provided with outlets of pneumatic means (19) to form a fluid cushion inside the bin (3) by means of fluid jets which converge to each other in an upward direction, the upper side of the cushion being situated at a distance above the exit slot (10) and the package of tape loops (2) floating on said cushion.