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The main parameters affecting the failure and deformation state of the rock mass around a circular opening are the level of vertical and horizontal in situ stresses, the characteristics of the rock mass, the diameter of the opening, and the support pressure. The influence of all these parameters on the stress-induced final deformations around circular openings was investigated by a finite difference based two-dimensional numerical simulation for both hydrostatic and nonhydrostatic stress field conditions. From the results of the parametric studies, the variation of tunnel strain versus the ratio of uniaxial compressive strength of the rock mass to in situ vertical stress and the ratio of radial support pressure to in situ vertical stress for fair quality and poor quality rock masses was statistically analysed. As a result of the three-dimensional nonlinear regression analysis and surface curve fitting process by means of a large number of models, a best-fit model with the best correlation with these dimensionless parameters was proposed for calculating tunnel strains and ground response curves. Specific charts were created to highlight the influence of parameters on the deformation response of the openings to various support pressures.Key words: numerical modelling, circular openings, ground response curve, finite difference, FLAC.