The stiffness and strength of the surrounding rock in underground caverns will deteriorate to a certain extent when it enters the plastic state. Based on the D-P yield criterion, the elastic-plastic solution for the anchored surrounding rock of deep-buried circular caverns is obtained considering the deterioration effects. The reliability of the method is verified by using the FLAC3D finite difference software, and the relevant influencing factors are analyzed. The results show that: (1) Considering the deterioration of the stiffness and strength of the anchored surrounding rock, the deformation of the surrounding rock is more realistic. (2) The residual cohesion c, the residual internal friction angle φ, the residual elastic modulus E have controlling effects on the anchorage plastic residual zone radius Rb and the wall displacement u. The larger the values of c, φ, E, the smaller the values of Rb and u, and vice versa. (3) The softening moduli Mc and Mφ have great influences on the radius Rb of the plastic residual zone and the wall displacement u, but the influences on the radius Rp of the plastic softening zone can be ignored. (4) Under the coordinated action of system bolt and support resistance pi, the scope of the plastic residual zone and the deformation of the surrounding rock can be effectively controlled.