Wrapping machine for wrapping a plastic foil web around an object, said wrapping machine comprising - a machine frame supported on a fixed base and comprising vertical upright columns, - a lifting frame arranged to be moved upwards and downwards in a vertical direction while guided by the upright columns, - a power means for moving the lifting frame, - a circular guide track supported on the lifting frame so as to be movable together with it, - a foil dispenser, on which a foil web roll can be rotatably mounted, said foil dispenser being arranged to circulate on a ring-like path, guided by the circular guide track, about the object to be packaged for delivering plastic foil web from the foil web roll to form a wrapping around the object to be packaged, and - a gripping and cutting device, which comprises: - a device frame; - a first swing arm, connected to the device frame by a first joint so as to be turnable between a horizontal position and a vertical position, and said first swing arm comprising a first holding device for gripping and holding the foil web, and a cutting device for cutting the foil web, and - a second swing arm connected to the device frame by a second joint disposed at a distance from the first joint so as to be turnable between the horizontal position and the vertical position, said second swing arm comprising a second holding device for gripping and holding a constricted foil web, characterized in that the gripping and cutting device is coupled to the lifting frame so as to be vertically movable together with it, and - the lifting frame comprises substantially horizontal guide rails (27, 28) along which the device frame can be moved horizontally to move the gripping and cutting device towards and away from the object to be wrapped; and a second power means for moving the device frame. - a machine frame supported on a fixed base and comprising vertical upright columns, - a lifting frame arranged to be moved upwards and downwards in a vertical direction while guided by the upright columns, - a power means for moving the lifting frame, - a circular guide track supported on the lifting frame so as to be movable together with it, - a foil dispenser, on which a foil web roll can be rotatably mounted, said foil dispenser being arranged to circulate on a ring-like path, guided by the circular guide track, about the object to be packaged for delivering plastic foil web from the foil web roll to form a wrapping around the object to be packaged, and - a gripping and cutting device, which comprises: - a device frame; - a first swing arm, connected to the device frame by a first joint so as to be turnable between a horizontal position and a vertical position, and said first swing arm comprising a first holding device for gripping and holding the foil web, and a cutting device for cutting the foil web, and - a second swing arm connected to the device frame by a second joint disposed at a distance from the first joint so as to be turnable between the horizontal position and the vertical position, said second swing arm comprising a second holding device for gripping and holding a constricted foil web, characterized in that the gripping and cutting device is coupled to the lifting frame so as to be vertically movable together with it, and - the lifting frame comprises substantially horizontal guide rails (27, 28) along which the device frame can be moved horizontally to move the gripping and cutting device towards and away from the object to be wrapped; and a second power means for moving the device frame.