Abstract: A riser pipe construction for a drilling connection from a drilling vessel to a valve previously provided on a sea floor comprises a riser pipe through which drilling means can be passed by means of which an oil well can be drilled as well as pressure pipes extending along the riser pipe to operate the valve, and floating elements disposed around the riser pipe and the pressure pipes to limit the load on the drilling vessel. The riser pipe and the pressure pipes are built up from modules capable of being coupled together, the floating elements are formed by steel tubular chambers closed so as to be gastight, disposed around the relevant modules and firmly connected thereto. The invention also relates to a riser pipe module.