The method relates to a riser comprising a main tube and auxiliary lines. Each tubular element forming the auxiliary lines is fastened at one end by a complete link with the central tube and at the other end by a link allowing a longitudinal play J with the central tube. The method provides adjustment of play J so that, on the one hand, during conventional drilling operations, the elements forming the auxiliary lines slide in relation to the central tube and, on the other hand, during show control or testing operations, the elements forming the auxiliary lines form hyperstatic assemblies with the central tube. The method thus allows to prevent buckling of the peripheral lines when they are under pressure because they work under hyperstatic conditions.