A capsule for making beverages, containing a powdered food substance which allows a beverage to be made by passing hot water through it, the capsule comprising: a cup-shaped containment body in turn comprising a tubular lateral wall extending between a first edge and a second edge, and a bottom portion connected to the first edge and extending transversally to a central axis of the tubular lateral wall, the bottom portion comprising a dispensing hole, and the containment body defining a containment chamber inside itself; a closing element fixed to the second edge for closing the top of the containment body; a lower filtering element mounted in the containment chamber and positioned between the powdered food substance and the bottom portion; and a sheet of flexible material, impermeable to oxygen, mounted in the containment chamber and fixed in an oxygen-tight way to the containment body, the sheet of flexible material comprising at least one first layer constituted of a film made of plastic material and one second layer constituted of an aluminium film, which are coupled to each other, and the sheet of flexible material also being positioned between the powdered food substance and the dispensing hole with the first layer interposed between the powdered food substance and the second layer; characterised in that the first layer comprises one or more cuts or through openings, and in that for each of said cuts or through openings the first layer comprises a dispensing zone that surrounds the related cut or through opening, the first layer being locally detached from the second layer at each dispensing zone, for allowing at each dispensing zone the second layer to swell towards the bottom portion until it bursts after an increase in pressure on the side of the first layer facing the powdered food substance. a cup-shaped containment body in turn comprising a tubular lateral wall extending between a first edge and a second edge, and a bottom portion connected to the first edge and extending transversally to a central axis of the tubular lateral wall, the bottom portion comprising a dispensing hole, and the containment body defining a containment chamber inside itself; a closing element fixed to the second edge for closing the top of the containment body; a lower filtering element mounted in the containment chamber and positioned between the powdered food substance and the bottom portion; and a sheet of flexible material, impermeable to oxygen, mounted in the containment chamber and fixed in an oxygen-tight way to the containment body, the sheet of flexible material comprising at least one first layer constituted of a film made of plastic material and one second layer constituted of an aluminium film, which are coupled to each other, and the sheet of flexible material also being positioned between the powdered food substance and the dispensing hole with the first layer interposed between the powdered food substance and the second layer; characterised in that the first layer comprises one or more cuts or through openings, and in that for each of said cuts or through openings the first layer comprises a dispensing zone that surrounds the related cut or through opening, the first layer being locally detached from the second layer at each dispensing zone, for allowing at each dispensing zone the second layer to swell towards the bottom portion until it bursts after an increase in pressure on the side of the first layer facing the powdered food substance.