A beverage capsule machine for making single use capsules for extract or infusion beverages, comprising a rigid, cup-shaped container having a bottom and an upper aperture provided with a rim, a dose of extract or infusion product contained inside the rigid container and a piece of sealing sheet for closing the upper aperture of the rigid container, the machine comprising: a transport element for transporting the rigid containers and being closed in a loop around movement means for moving the transport element; the transport element being configured to define a plurality of pockets for receiving the rigid containers and which are positioned one after the other, in sequence, each having a respective vertical axis; a plurality of stations which are positioned along a feed path followed by the transport element and which are configured for operating in phase with the same transport element and comprising: a feeding station for feeding the rigid containers into respective pockets of the transport element; a dosing station for filling a dose of product into the rigid container; a closing station for closing the upper aperture of the rigid container with the piece of sealing sheet; and an outfeed station which withdraws the formed capsules from the transport element; characterized in that the closing station comprises at least: - a unit for preparing and feeding single pieces of sealing sheet correlated with the shape of the upper aperture of the rigid container; - transfer means by which individual pieces of sealing sheet are withdrawn sequentially and continuously from the preparing and feeding unit and by which the pieces of sealing sheet are transported and delivered to a corresponding pickup element of - a sealing wheel which is adapted to seal the piece of sealing sheet to the rigid container, is rotatable continuously about a first vertical axis along a rotational path and is equipped around its circumference with a plurality of pickup elements provided with corresponding sealing units; the sealing units on the wheel being configured to be placed, in phase coordination, on top of a corresponding rigid container on the transport element in such a way as to join the piece of sealing sheet to the rigid container along a stretch of the feed path of the transport element comprising a stretch, of the rotational path of the sealing wheel in phase synchrony with the transport element itself. - a unit for preparing and feeding single pieces of sealing sheet correlated with the shape of the upper aperture of the rigid container; - transfer means by which individual pieces of sealing sheet are withdrawn sequentially and continuously from the preparing and feeding unit and by which the pieces of sealing sheet are transported and delivered to a corresponding pickup element of - a sealing wheel which is adapted to seal the piece of sealing sheet to the rigid container, is rotatable continuously about a first vertical axis along a rotational path and is equipped around its circumference with a plurality of pickup elements provided with corresponding sealing units; the sealing units on the wheel being configured to be placed, in phase coordination, on top of a corresponding rigid container on the transport element in such a way as to join the piece of sealing sheet to the rigid container along a stretch of the feed path of the transport element comprising a stretch, of the rotational path of the sealing wheel in phase synchrony with the transport element itself.