A machine for making single use capsules (1) for extract or infusion beverages includes: a transport element (8) for transporting rigid containers (2) and being closed in a loop around movement apparatus (9); a feeding station (11) for feeding the rigid containers (2) into respective pockets (10) of the transport element (8); a dosing station (12) for dosing the product into the rigid container (2); a closing station (13) for closing the rigid container (2) with a piece of sheet (7); an outfeed station (14). The closing station (13) includes a unit (500) for preparing and feeding single pieces of sealing sheet (7) correlated with the shape of the upper aperture (4) of the rigid container (2); transfer apparatus (17) by which individual pieces of sealing sheet (7) are withdrawn sequentially and continuously from the preparing and feeding unit (500) and by which the selfsame pieces (7) are transported and delivered to a sealing wheel (19) adapted to seal the piece of sealing sheet (7) to the rigid container (2).