Abstract: A process and a machine for packaging items in stretchable foils of plastic material, wherein the foil is subjected to maximum stretching in at least a transversal direction, before bringing the item to be packaged into contact with the thus pre-stretched foil. To avoid further stretching of the pre-stretched foil, the machine comprises a lifting table for vertically elevating the item relative to the pre-stretched foil, and means for controllably releasing at least the transversal opposed foil side edges as the lifting table moves upwardly, while folding the side edges under the item.