At the end of the year 2001 the radiolytic gases hydrogen and oxygen accumulated and exploded in non-vented steam pipelines at two nuclear power plants. The HELIO code has been developed for the numerical simulation and analyses of these incidents and as a support to the prescription of safety measures. This paper presents modelling and numerical approach, verification and results of the two-dimensional module of the HELIO code for the conditions of hydrogen-oxygen accumulation in a vertical pipe closed at the top. The results show a dynamics of hydrogen-oxygen accumulation, formation and propagation of the concentration front, gas mixture natural convection due to concentration and temperature imposed buoyancy forces and gas mixture-liquid film interface shear. The verification against plant data and for the common problem of steam condensation in the presence of air is presented. (C) 2004 Elsevier Ltd. All rights reserved.