Improvement of operating conditions of existing circulating fluidised bed combustor units, as well as attempts to scale up present units to larger ones, are mainly based on empirical correlation or simplified scaling laws. Moreover, it is known that the details of the unit geometry (entry and exit design, horizontal cross-section shape, secondary air location and configuration) have a great importance in the overall plant performance. Improvement of our understanding of the complex hydrodynamic behaviours involved in these processes requires refined and local physical models. The approach retained at the Laboratoire National d'Hydraulique of EDF for the prediction of the two-phase flows in complex geometries is based on the two-fluid model formalism, where both phases are characterised by their first velocity moments (volumetric concentration, mean velocity and second order fluctuating velocity correlation tensors). Separate transport equations are written for each moment with appropriate closure assumptions for unknown terms such as the momentum exchange between the two phases and the effective stress tensors of both phases. These closures are based on the existing kinetic theory of dry granular media and on single phase turbulence modelling. The present paper will try to focus on the closure of the solid stress based on the kinetic theory. By starting from the "simplest case" of a dry assembly of spherical particles, with one diameter, we will see that the kinetic theory provides us an appropriate formalism and some practical closures. These can be easily checked by performing some direct simulation of a set of particles. Nevertheless, in industrial applications, the particles size distribution cannot be reduced to a narrow peak distribution (one size) but in some case to a wide Gaussian distribution, the variance sometimes be compared to the mean diameter; in some other cases, the distribution can be compared to well separated picks. For each of these cases, the kinetic theory provides a conceptual formalism but the derivation of practical closures requires some restrictive assumptions leading to important limitations in the range of applicability of these closures. Moreover, another important assumption underlying these closures is that particles are freely moving between collisions. Of course, in real gas-solid flow, the carrier gas acts on each particle through the drag force. By introducing this force in the kinetic theory, it is possible to modify the closures and direct numerical simulations are able to validate these modifications. Another assumption underlying these closures is that colliding particles are not correlated. Nevertheless, the interstitial carrier gas or interparticle forces can introduce a correlation between neighbouring particles. In the present paper, we will try to emphasise these limitations and to indicate some possible way to overcome these limitations.