A laser cutting machine (1) for metal sheets (2), in which a laser cutting station (5) is arranged between a sheet loading store (26) and an unloading store (27) arranged below the work surface (4), an intermediate portion (17) of which is arranged at the laser cutting station (5) and is provided with a door (18) that may be opened in order to unload the cut parts of sheet (2), a first portion (14) may be moved from and towards a closed position of the un loading store (26), and a second portion (15) may be moved from and towards a closed position of the unloading store (27); an extraction device (42) being provided to selectively lift the metal sheets (2) from the loading store (26) at least partially above the work surface (4) when the first portion (14) is arranged in an open position.