In order to load and discharge pieces of sheet metal automatically onto and from a machine tool (20) having a horizontal table (26) movable along a first horizontal axis (X), a horizontal discharge table (52) and a horizontal loading table (58) are provided in positions in which the tables are side by side and substantially aligned with the horizontal plane of the table (26) of the machine tool (20). An unprocessed piece of sheet metal to be supplied to the machine tool (20) is placed on the loading table (58). Initially, the piece-holding table (26) of the machine tool (20) is positioned beside the discharge table (52). The piece of sheet metal (30) on the piece-holding table (26) is transferred to the discharge table (52) by being slid on the bearing surfaces of the tables in the direction of a second horizontal axis (Y) perpendicular to the first axis (X). The table (26) of the machine tool (20) is then moved to a position in which it is beside the loading table (58). The unprocessed piece of sheet metal situated on the loading table (58) is then transferred to the piece-holding table (26) by being slid on the bearing surfaces of these tables.