Chimney failures in the overburden may occur as a result of urban tunnelling or mining activities. Propagation of these failures has undesirable effects both underground and on the surface. These failures may be attributed to a number of distinct mechanisms, each associated with different geological environments. These mechanisms are usually connected with shallow cover, weakness in the crown of an opening, insufficient cover to overlaying permeable water bearing strata, etc. Furthermore, they can also be due to vertical fissures, pipes and man made features, such as wells or sewer constructions. At the underground level a range of effects may be evident such as instability of the sides of the opening, popping of the face, or explosive failure of the soil / rock mass. When such failures propagate to the surface, consequences there may also be severe depending on the specific conditions. In this paper, soil / rock mass parameters that may lead to chimney failure of the face of shallow underground openings are investigated using the finite element method. Both elastic and elastoplastic solutions are presented with a measure of the expected deformations.