Stochastic approach has been applied to formulating a set of equations of motion which, together with some auxiliary correlations, constitute a mathematical framework suitable for modelling and analysing of the three-dimensional flow field of gas stream within voids of granular catalyst bed packed in a tube. The framework links the interstitial and the superficial flow fields inside the tube. Consequently, the framework has been verified and its empirical parameters have been estimated by computing the interstitial flow field characteristics on the ground of the radial profiles of the local superficial velocity vectors three components measured at the bed outlet cross-section and of the bed voidage taken from literature experimental data. The correctness of the framework has been confirmed by satisfactory agreement, +/- 5%, between the average interstitial axial velocity determined by numerical integration of the radial profiles of the local values predicted and that resulted from the rotameter measurements and the bed average free cross-section in individual experiments. (c) 2005 Elsevier B.V. All rights reserved.