Machine for stabilising palletised loads includes a functional arrangement, a first movement apparatus generating relative motion about a revolution axis, a second movement apparatus generating relative translation motion of the functional arrangement in a direction parallel to the revolution axis. The functional arrangement includes a support shaft, a motorised drive roller, a contrast roller, and actuator members to create relative movement between the drive roller and the contrast roller in transversal direction with respect to the respective rotation axes between a distanced configuration, in which a gap is defined between the drive roller and the contrast roller to be crossed with clearance by the covering tape unwinding from the reel, and a neared configuration, in which the drive and contrast rollers clamp the covering tape. The support shaft and the contrast and/or drive rollers are mounted on the functional arrangement and oriented in the same direction.