A packaging machine for wrapping groups of products in a roll, comprising at least: - a packaging unit positioned close to a feed channel; the unit having a conveyor equipped with a plurality of pockets, each of which has the shape of an inverted "U" and which can be positioned, in sequence, facing the feed channel; - a transfer element configured for feeding, in a feed direction, to the pockets of the packaging unit, the groups of products in a roll with a corresponding sheet of wrapping material; the transfer element having movement means configured for moving, at a first speed, the transfer element at least from a first operating position, for receiving the groups of products in a roll, to a second operating position releasing the group of products in a roll and the sheet of wrapping material intercepted by the group of products to the corresponding pocket of the packaging unit; - feed and positioning units configured for feeding the sheet of wrapping material inside the vertical channel, in a direction transversal to the direction for feeding the group of products; - means for controlled retaining and unwinding of the sheet of wrapping material positioned along the feed channel; characterised in that it comprises: - a first movement unit connected to the controlled retaining and unwinding means and configured to move the controlled retaining and unwinding means from a position of free passage of the sheet of wrapping material to a position for bilateral retaining of the sheet of wrapping material positioned in the feed channel; - a second movement unit connected to the controlled retaining and unwinding means and configured to move the controlled retaining and unwinding means, located in the retaining position, so as to unwind the sheet of wrapping material in a controlled manner and at the movement of the transfer element from the first operating position to the second operating position. - a packaging unit positioned close to a feed channel; the unit having a conveyor equipped with a plurality of pockets, each of which has the shape of an inverted "U" and which can be positioned, in sequence, facing the feed channel; - a transfer element configured for feeding, in a feed direction, to the pockets of the packaging unit, the groups of products in a roll with a corresponding sheet of wrapping material; the transfer element having movement means configured for moving, at a first speed, the transfer element at least from a first operating position, for receiving the groups of products in a roll, to a second operating position releasing the group of products in a roll and the sheet of wrapping material intercepted by the group of products to the corresponding pocket of the packaging unit; - feed and positioning units configured for feeding the sheet of wrapping material inside the vertical channel, in a direction transversal to the direction for feeding the group of products; - means for controlled retaining and unwinding of the sheet of wrapping material positioned along the feed channel; - a first movement unit connected to the controlled retaining and unwinding means and configured to move the controlled retaining and unwinding means from a position of free passage of the sheet of wrapping material to a position for bilateral retaining of the sheet of wrapping material positioned in the feed channel; - a second movement unit connected to the controlled retaining and unwinding means and configured to move the controlled retaining and unwinding means, located in the retaining position, so as to unwind the sheet of wrapping material in a controlled manner and at the movement of the transfer element from the first operating position to the second operating position.