This paper describes the method of modelling and numerical simulation of bubble column bioreactors in which the process of aerobic biodegradation of carbonaceous substrate occurs. Such bioreactors belong to systems with distributed state variables. Determining steady states of such objects results in solving non-linear boundary-value problems. The bioreactors with axial dispersion and piston flow with biomass recirculation were analysed. The effectiveness of selected algorithms used to determine the steady states of such bioreactors were compared; the numerical properties of mathematical models of analysed bioreactors were specified, the branches of steady states in bioreactors with axial dispersion and piston flow were determined and the application areas of such bioreactors were defined. (c) 2010 Elsevier Ltd. All rights reserved.