A unit for picking-up a flattened tubular blank and for opening out the blank has gripping devices borne by a pick-up member, a frame, and a first arm hinged to the frame and to the pick-up member. A second arm is hinged to the frame, at a hinge axis being arranged at a lower height than the first arm hinge axis. A third arm is hinged to the second arm and which to the pick-up member. The first arm and the second arm are activatable in phase relation with one another. The unit is configured such that the pick-up member picks up the flattened tubular blank from the pick-up position (P), rests the tubular blank on a rest plane, and opening-out the tubular blank. The unit then moves the pick-up member towards the pick-up position (P), passing over the opened-out tubular blank.