A sticky sheet which is to be disposed of is fed in a first direction parallel to its surface so that its leading edge abuts against a stopper construction. The sticky sheet is then further fed in the first direction and is folded up in a second direction substantially perpendicular to the first direction into several layers against the stopper construction, these layers resting upon a plane support construction which extends from the lower part of the stopper construction in the direction opposite to the first direction. Then the superposed layers of the folded sticky sheet are moved in a third direction substantially perpendicular to the first and second directions while being compressed together so as to stick them together so as to be disposed of in the form of a relatively thick and narrow strip including several superposed layers which are adhering together due to their stickiness. A machine is also disclosed for disposing of a sticky sheet in the above described way.