Dynamic analysis of risers often requires consideration of large deflections. One of the discretisation methods which includes analysis of large deflections is the rigid finite element method (RFEM). This paper presents a new, numerically effective, planar formulation of the method. The model takes into account large deflections caused by bending and longitudinal flexibilities. The models elaborated are, after validation, applied in calculations of static deflections and analysis of free frequencies of risers. Investigations are concerned with how a riser’s parameters (such as length and top/bottom supports), the sea current and internal flow all influence frequencies of free vibrations. Analysis of dynamics of a riser with and without an additional mass attached to the bottom of the riser is also carried out.