Closed form solutions assume opening shape to be circular to simplify the calculation of the ground response curve for the design of underground openings. However, in mining and civil engineering works, non-circular openings are commonly excavated. Therefore, there is a need to estimate the ground response curve for such openings. In this respect, a simple model for circular, arch and rectangular shape underground openings subject to a hydrostatic stress field is the aim of this study. A comprehensive numerical modelling, using the finite difference method, based on numerical modelling code FLAC version 4.0, was carried out. in addition to shape of an opening, the effect of rock mass strength, opening size, in situ stress on strain (tunnel deformation to tunnel radius) of the opening in response to applied support pressures was investigated parametrically by developing models for each specific condition. The strain results for each excavation shape obtained from this large number of models against the normalized strength of rock mass and internal support pressure with in situ stress magnitude were evaluated by multiple regression analysis. As a result, a model that was well correlated to data was developed for an overall estimate of the ground response curve depending on relevant effecting parameters. The regression coefficients of the model were given for estimating both roof and sidewall response curve of each excavation shape. The model was verified by statistical tests and by an analytical solution. Diagrams were also established to highlight the influence of relevant parameters and to estimate the support pressure for a stable opening staying within the acceptable limits of strain. Strains occurring in a rectangular opening are found to be larger than those in the arch and circular openings for the other fixed parameters. In the mean time, larger strains occur around an arch shape opening than a circular opening.