Abstract: The tight connection fitting for a circular orifice in a rigid element is composed of a pipe in flexible material, such as rubber, whose external diameter is slightly greater than the bore of the orifice, and of a truncated cone-shaped bushing whose angle of conicity is less than the angle of friction between the two materials constituting the bushing and the pipe, and whose diameter at the base of the cone is substantially equal to the internal diameter of the pipe.The angle of conicity is, for a bushing in polyamide and a pipe in rubber, at the most 20.degree., and preferably between 2.degree. and 10.degree..The bushing is introduced into the pipe so that the head of the bushing is at a certain distance from the end of the pipe; that end of the pipe is introduced by force into the orifice, and then the bushing is caused to slide inside the pipe until it is blocked in.