A novel theoretical treatment is presented for simulating the shape of the wavy surface of thin liquid falling films, flowing freely inside a vertical pipe. The simulation proved particularly successful for the range similar to 800 less than or equal to Re less than or equal to similar to 5000. This is a regime where each one of the film main elements-roll waves, ripples, capillary waves and substrate-can be effectively used to adjust a different statistical characteristic of the film. The geometrical profile of all types of waves is simulated fairly well by a log-normal function with its parameters related to specific wave features. The Gaussian fashion of selecting the wave parameters from specific ranges of values and the subsequent random deposition of the produced waves over the film substrate attests the stochastic nature of falling films. The performance of the code routine is satisfactory producing considerably good reconstructions of the film surface shape for all the data sets used to assess its accuracy. The potential for appraising several obscure features of falling films by matching the experimental and theoretical results is discussed. (C) 2004 Elsevier Ltd. All rights reserved.