We consider axisymmetric fluid flow down the exterior of a rigid straight vertical cylinder and model the emergence and propagation of the finite-amplitude waves that are created at the free surface. A system of evolution equations for the film thickness and volumetric flow rate, that was first derived by Trifonov [1992. Steady-state travelling waves on the surface of a viscous liquid film falling down on vertical wires and tubes. A.I.Ch.E. Journal 38, 821-834] has been re-formulated as an extension of the classical falling film problem. To inspire confidence in the predictions of this model, its linear stability characteristics versus those of the full Navier-Stokes equations are examined yielding very good agreement. Travelling wave solutions are determined and analysed in detail over a wide range of system parameters. The solutions resemble those associated with film for sufficiently small film thickness to fibre radius ratios, and beads when these ratios are relatively large. Transient computations are also performed for comparison with the travelling wave solutions and demonstrate the selection mechanism leading to the development of so-called 'dominating' waves for comparison with experimental observations. (c) 2006 Elsevier Ltd. All rights reserved.