Rotated, circular arc geometry models have been developed to describe core-flow and vertical rat-holes in cylindrical hoppers and silos. The conceptual problem of the variation of incremental element thickness has been overcome, resulting in models of greater theoretical rigour. Models have been developed in an average stress and point stress form. Analysis shows that stresses vary with vessel radius through an arc angle parameter, epsilon, as well as with bed depth. The models indicate that conditions at a rat-hole annulus wall are quite different from the mean stress or wall stress and this has implications for stability and flow. A modified failure criterion, based upon azimuthal stress has been used to assess the stability of deep rat-holes, and a range of rat-hole stability deter-mined, which is dependent upon material properties and vessel diameter. Predicted stress distributions are functions of assumed internal stress distribution relationships. More physical data are required in this area to enable reliable modelling. (c) 2005 Elsevier B.V. All rights reserved.