Abstract: A fitting piece for connecting rigid or flexible tubes which are made particularly from plastic, the fitting piece having an opening to receive therein the tube and being provided with at least one inwards protruding annular rib having edges, preferably sharp edges, the cross-section of said rib being formed in such a manner that a straight line interconnecting the center point of the basis to the peak of the cross-section is inclined to the axis of the tube-receiving opening by an acute angle with its vertex pointing to the interior of said opening, said fitting piece being characterized in that at least the annular rib and preferably the whole of the fitting piece is made from an elastically deformable plastic material whose coefficient of elasticity amounts to at least 20,000 kgf per cm.sup.