The regression analysis method is being widely adopted to analyse the tunnel strain, most of which ignore the strain-softening effect of the rock mass and also fail to consider the influence of support pressure, initial stress state, and rock mass strength classification in one fitting equation. This study aims to overcome these deficiencies with a regression model used to estimate the tunnel strain. A group of geological strength indexes (GSI) are configured to quantify the input strength parameters and deformation moduli for the rock mass with a quality ranging from poor to excellent. A specific numerical procedure is developed to calculate the tunnel strain around a circular opening, which is validated by comparison with those using existing methods. A nonlinear regression model is then established to analyse the obtained tunnel strain, combining twelve fitting equations to relate the tunnel strain and the factors including the support pressure, the GSI, the initial stress state, and the critical softening parameter. Particularly, three equations are for the estimation of the critical tunnel strain, the critical support pressure, and the tunnel strain under elastic behaviour, respectively; and the other nine equations are for the tunnel strain with different strain-softening behaviours. The relative significance between the GSI, the initial stress and the support pressure on the tunnel strain is assessed.