Abstract: A fragmentable compression device for the anastomosis of hollow organs of the human body comprising free cylindrical members that are composed of sectors. The edges of the hollow organs to be anastomosed are compressed between the first and second members by means of the third member, which presses the second member against the first one. The first member is in turn composed of a first and second sub-members, said sub-members being composed of sectors the second one of said sub-members being locked within the first one by means of teeth that are present on the outer surface of the second sub-member, said teeth being inserted into notches that are carved out of the internal surface of the first sub-member.