The paper examined the steady-state multiplicity behaviour of the porous, non-isothermal, finite cylindrical catalyst pellet in the absence of external transport resistances. A numerical multigrid continuation technique with the preconditioned conjugate gradient squared as coarse grid solver was used. The numerical methods proved to be efficient and reliable so that computations with fine grids (up to 129 x 129 grid points on the unit square) are easily performed. The key parameter of the investigation is the reaction parameter. The effect of the other governing parameters (especially the aspect ratio) was also analysed. An infinite number of steady states, with a scenario different from that usually used to explain this situation, were obtained at small values of the aspect ratio (the height of the cylinder is greater than the diameter of the cylinder). (c) 2006 Elsevier Ltd. All rights reserved.