A beverage capsule machine for making single use capsules for extract or infusion beverages such as coffee or tea, 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 length of sheet for closing the upper aperture of the rigid container, the machine comprising: a transport element for transporting components of the capsule 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 components of the capsule and which are positioned one after the other, in succession, each having a respective vertical axis; a plurality of stations which are positioned along a path followed by the transport element and which are configured for operating in phase with the same transport element and comprising: a feed station for feeding the rigid containers into respective pockets of the transport element; a dosing station for dosing the product into the rigid container; a closing station where the upper aperture of the rigid container is closed with a length of sheet; an outfeed station which withdraws the capsules from the transport element; characterized in that one or more of the stations (11, 12, 13, 14) comprises: - at least one picking point where components of the capsule placed on top of each other in a stack are picked up; - at least one contact head for picking and detaching a component from the bottom of the stack at the picking point and placing the component on the transport element; - movement means for moving the at least one contact head from a first, advanced position configured both to contact and pick the component and also to place the component on the transport element, to a second, withdrawn position when the contact head is in transit, wherein passing from the first, advanced position to the second withdrawn position, the contact head extracts the component from the stack, and wherein passing from the second, withdrawn position to the first, advanced position, the contact head places the component in a respective pocket of the transport element; - a wheel designed to rotate the at least one contact head and the movement means and configured to operate in phase therewith and with the transport element and to carry the at least one contact head from the picking point to a transit zone of the transport element along a first movement path (P24A), and from the transit zone of the transport element to the picking point along a second movement path (P24R). - at least one picking point where components of the capsule placed on top of each other in a stack are picked up; - at least one contact head for picking and detaching a component from the bottom of the stack at the picking point and placing the component on the transport element; - movement means for moving the at least one contact head from a first, advanced position configured both to contact and pick the component and also to place the component on the transport element, to a second, withdrawn position when the contact head is in transit, wherein passing from the first, advanced position to the second withdrawn position, the contact head extracts the component from the stack, and wherein passing from the second, withdrawn position to the first, advanced position, the contact head places the component in a respective pocket of the transport element; - a wheel designed to rotate the at least one contact head and the movement means and configured to operate in phase therewith and with the transport element and to carry the at least one contact head from the picking point to a transit zone of the transport element along a first movement path (P24A), and from the transit zone of the transport element to the picking point along a second movement path (P24R).