A method of installing and implementing a rigid tube (10) referred to as a “main” tube, wherein the following steps are performed: a) lowering an end of the main tube from a floating support or vessel (13) on the surface (14) to below sea level (14) to be connected to undersea equipment (16) that is immersed (17); and b) maintaining the main tube as immersed in this way for a given period of time. The said main tube (10) is caused to pass through a cylindrical orifice (4) of circular section in a stress limiter device, the orifice having a slippery internal coating (3) secured to a support structure (9) secured to the floating support or vessel, the service tube thus being suitable for sliding in contact against the slippery coating during steps a) and b).