As soon as an underground excavation is made, the in situ stresses within the rock mass gets disturbed and redistribution of stresses takes place. As such, the stresses around an underground opening would be different from the pre-excavation stresses, i.e., in situ stresses. A zone of disturbed stresses is formed around an opening and generally known as 'zone of influence'. The extent of zone varies from rock to rock. For a very good and strong rock this zone is small, where as for weak rocks it is large. In other words, if the induced stresses due to tunnelling do not exceed the in situ strength of the rock mass, the surrounding rock mass remains in an elastic state and the zone of influence is limited. However, when the induced stress is more than the strength of the rock mass, the rock fails and the condition is popularly known as squeezing ground condition. The boundary stresses around an underground opening govern the stability of underground opening. It has been studied by Hoek and Brown (1982) that the shape of underground opening does affect the boundary stresses around an underground opening. To carry forward the work, a Research Project was awarded to the author by Ministry of Water Resources, Government of India. Parametric study has been carried out to obtain the influence of shape of underground openings on maximum boundary stress. In addition to five different shapes of the opening, various other parameters used for the study are tunnel depth, in situ stresses, uniaxial crushing strength of intact rock material, and Bieniawski's rock mass rating. The analyses for various values of all these parameters have been performed using numerical analysis code FALC3D. The maximum boundary stresses at the roof have been obtained and simple equations are developed for estimating the maximum boundary stresses. The analysis shows that the curves for horse-shoe and circular shapes are almost superimposing indicating that the roof stresses at the centre of the opening in these two shapes are almost same. Using the equations, maximum boundary stress can be estimated. Using the failure criterion of Sheorey (1997), safety factor contours for all the models have been plotted and the minimum safety factor values (fmin) at the roof have been obtained. Using fmin, in situ stress ratio k, depth of underground opening, rock mass rating RMR and laboratory crushing strength, rc, finally different equations have been developed for each shape to estimate the minimum factor of safety value in the roof of the opening. (A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E124500.