The excavation of the cavern is accompanied by the deterioration of the parameters of the rock mass, and it is of great significance to describe the deterioration of the parameters to guide the engineering practice. In order to describe the deterioration of the deformation parameters, based on the Hoek-Brown criterion, the damage threshold is used to characterize the degree of deterioration of the elastic modulus, and the equilibrium equation with the damage threshold is simplified by the Taylor series to obtain the analytical solution of the radius of the plastic zone and the damage threshold is given. The value method, combined with the finite difference software FLAC3D, verifies the rationality of the formula. Based on the two assumptions of constant elastic strain and variable elastic strain, the plastic zone displacement expression including the damage threshold is obtained by combining the uncorrelated flow criterion. Finally, the variation law of the radius of plastic zone and the displacement of the cave wall under different parameters is analyzed by an example. The results show that the more serious the deterioration is, the easier the cavern is to be unstable. As the damage threshold increases, the displacement difference and plastic zone radius under the two assumptions gradually increase, and the displacement obtained by the constant elastic strain assumption is smaller. In order to avoid instability and damage of the cavern, support should be provided in time.