Abstract A parametric study has been carried out using the numerical analysis code FLAC 3D to obtain the influence of various shapes of underground openings on the maximum induced boundary stress. Five shapes—viz. circular, horseshoe, rectangular, elongated D-shape and elliptical—have been considered. For each shape, four tunnel depths and five horizontal in situ stress models have been taken for the study of induced boundary stresses. The values of maximum and minimum induced boundary stresses in the roof and wall have been obtained from the analyses. This data has subsequently been used to develop correlations to estimate the normalized maximum and minimum boundary stresses, which have been subsequently compared with the strength of the rock mass obtained from the Sheorey's non-linear failure criterion for three rock masses represented by three values of Bieniawski's RMR and three values of crushing strength of intact rock material. The values of minimum factor of safety at the roof and the wall have been collected from all the plots. Using these data sets, different correlations have been developed to estimate the minimum factor of safety ( f min) in the roof and wall. Since the bolt length should be normalized with the opening size, some more computer models have been run with varying tunnel width of 5 and 20 m besides the earlier 10 m size to obtain the correlations for estimating the bolt length. The depth of factor of safety contour of 1.5 from the opening periphery has been picked up from all these models and the correlations have been developed for estimating the roof and wall bolt length for the five shapes of underground openings. The correlations for bolt length show that in addition to the shape of underground openings and in situ stress, the bolt length also varies with the rock mass type. These correlations have been verified for field cases of elongated D-shape openings.