A wipe material dispensing machine includes a housing forming a receptacle with a back plate, a horizontal lower wall, side walls, and an articulated lockable cover. The inner face of the cover has a protruding curved member. A device, articulated relative to the housing, fulfils the functions of loading, guiding and preventing creasing of the pre-cut strip of material which is pulled so that it can be removed from the forward, lower part of the machine. The device includes a raised curved element surrounding the member on the cover when the cover is closed. The element and member being concentric and leaving room for the pulled pre-cut strip of material to pass through. The pre-cut wipe material is wound on a reel or accordion pleated, and the lower part of the machine includes, at the point where the material emerges, opposite-facing limit stops.