Summary: The lumped mass discretization method is used to derive the equations of motion of flexible risers in three dimensional space. Nodal shear forces and bending moments are included in the formulations and fluid loading on the structure is calculated using the Morison equation. A simple model of the sea bed contact for catenary risers is given and tested. Nonlinear equations describing the riser motions are solved in the time domain using the tangent stiffness incremental approach combined with the Wilson-theta numerical integration algorithm. Computational efficiency is improved via a compact ‘profile storage’ technique, used for the assembly of element matrices, given by R. L. Taylor [Computer procedures for finite element analysis, in The Finite Element Method (Ed. by O. C. Zienkiewicz), 3rd Ed. (1977; Zbl 0435.73072)]. Consideration is also given to natural periods and mode shapes for small oscillations about the static equilibrium position of the riser. Comparison of results with experimental values, analytical solutions and independent results from the published literature show very good agreement.