SUMMARYMany analysts use simple lower-order beam elements for the non-linear analysis of curved beam and arch structures. The aim of the present paper is to indicate how one may add the e ects of buoyancy, steady-state current loading and riser top-tension to such an idealization so that it may be used for the analysis of o shore pipes and risers. The current work is restricted to static two-dimensional modelling but it paves the way for further work in three dimensions, which will include dynamics.