Machine for packaging products of the tobacco industry, particularly snus, comprising: - at least one conveyor for feeding a plurality of containers containing the products along a conveying path; - a unit for feeding packages along a feeding direction; characterised by - an overturning unit which is arranged along the conveying path and which comprises: - a rotor comprising a first housing, for receiving at least one first container, and a second housing for receiving at least one second container, the rotor being rotatable around a horizontal rotation axis for making the first and the second housing (22, 23) reciprocally swap positions, between a first position for loading the containers and a second position for unloading the products from the containers, into the packages that are fed along the feeding direction, - at least one first closing member (25A, 25B) for closing an upper opening (100A', 100B') of the container positioned in the first housing, and at least one second closing member (26A, 26B) for closing an upper opening (100A', 100B') of the container positioned in the second housing, the at least one first closing member (25A, 25B) and the at least one second closing member (26A, 26B) being mounted on the rotor so as to be movable between a closing position and a position for opening the containers, and - a control unit, which is configured to command the first or the second closing member (25A, 25B, 26A, 26B) to the opening position so as to unload the products through the upper opening of the container that is positioned in the first or second housing (22, 23), when the first or the second housing (22, 23) is in the unloading position. - at least one conveyor for feeding a plurality of containers containing the products along a conveying path; - a unit for feeding packages along a feeding direction; characterised by - an overturning unit which is arranged along the conveying path and which comprises: - a rotor comprising a first housing, for receiving at least one first container, and a second housing for receiving at least one second container, the rotor being rotatable around a horizontal rotation axis for making the first and the second housing (22, 23) reciprocally swap positions, between a first position for loading the containers and a second position for unloading the products from the containers, into the packages that are fed along the feeding direction, - at least one first closing member (25A, 25B) for closing an upper opening (100A', 100B') of the container positioned in the first housing, and at least one second closing member (26A, 26B) for closing an upper opening (100A', 100B') of the container positioned in the second housing, the at least one first closing member (25A, 25B) and the at least one second closing member (26A, 26B) being mounted on the rotor so as to be movable between a closing position and a position for opening the containers, and - a control unit, which is configured to command the first or the second closing member (25A, 25B, 26A, 26B) to the opening position so as to unload the products through the upper opening of the container that is positioned in the first or second housing (22, 23), when the first or the second housing (22, 23) is in the unloading position. - a rotor comprising a first housing, for receiving at least one first container, and a second housing for receiving at least one second container, the rotor being rotatable around a horizontal rotation axis for making the first and the second housing (22, 23) reciprocally swap positions, between a first position for loading the containers and a second position for unloading the products from the containers, into the packages that are fed along the feeding direction, - at least one first closing member (25A, 25B) for closing an upper opening (100A', 100B') of the container positioned in the first housing, and at least one second closing member (26A, 26B) for closing an upper opening (100A', 100B') of the container positioned in the second housing, the at least one first closing member (25A, 25B) and the at least one second closing member (26A, 26B) being mounted on the rotor so as to be movable between a closing position and a position for opening the containers, and - a control unit, which is configured to command the first or the second closing member (25A, 25B, 26A, 26B) to the opening position so as to unload the products through the upper opening of the container that is positioned in the first or second housing (22, 23), when the first or the second housing (22, 23) is in the unloading position.