Abstract: The constitutive descriptions of concrete materials idealize the pressure-volumetric strain relationship as the tri-linear equation of state and idealize the shear strength-pressure relationship as the Mohr-Coulomb yield criterion considering the tension cutoff and the shear saturation. The dynamic response expression of the spherical cavity expansion is derived by the self-similar methods, and the dynamic response numerical solution is given by the Runge-Kutta-Felberg method. The result shows that the cavity expansion pressures increase with the cavity expansion velocity and the shear saturation strength, and the cavity expansion pressures considering the shear saturation are less than those without considering the shear saturation in case of the high cavity expansion velocity.