The pinching device includes two cross-sections, each having a hollow part with a male indentation and a female indentation, and locking elements, whereby the surfaces of the indentations form a positive pinching passage of the tube; the male indentation has a U shape with a core and two wings; the female indentation has a U shape with a core and two wings; and the pinching passage has a U shape with a core and two wings; the two opposite wings will draw together toward their ends that are opposite to the cores of the indentations, and each of the two wings of the pinching passage has an opening whose width will diminish towards its end that is opposite to the core of the pinching passage; the width of the opening of the pinching passage is at most slightly smaller than twice the thickness of the wall of the flexible tube to be pinched, and, designed to constitute a pinching closing device, it is disposable, performing a function of closing the tube on itself in the pinching region, preventing any passage of fluid into the tube.