Process for closing and cutting into sections a flexible tube, with a cutting element and a pinching closing device for cutting into sections with two cross-sections, each with two parts with indentations that can be placed in removable extension by combination elements and that make a passage with an access, whereby the pinching closing device is in the open or closed state where the cross-sections are closed by locking members and where the surfaces form a pinching closing passage of the tube; the pinching region of the tube is positioned in the indentation of a cross-section; the other cross-section is brought opposite the preceding one and the pinching closing device in the closed state, with cooperation of the locking elements, the tube being positively pinched and closed in two positive pinching zones, and thus held in place; the tube is cut into sections between the parts in the closed state, using the cutting element by passing it into the passage without it interfering with the pinching closing device; and the parts are dissociated.