In this study the influence of the consolidation stress on the bulk density of dusts separated from the off-gas of a broad variety of industrial processes was investigated. With the exception of very small values of the stress this dependence can be approximated very well by a simple function. One coefficient in this function correlates very well with the bulk density measured according to EN ISO 60, while the other coefficient shows a good correlation with a function, combining several dust properties. Using this approximation function equations for the vertical stress and bulk density in the shaft of a cylindrical silo as a function of the distance from the surface were derived. The results for the vertical stress and the mass of the bulk obtained with these equations were compared with those acquired on the basis of Janssen's equation assuming constant bulk density according to EN ISO 60 and a constant average bulk density. Up to a certain distance from the surface of the bulk the values for the stress and for the mass were between the results obtained by the two variants with constant bulk density, whereas for greater distances the resulting values were higher.