The collapse of cavities under shock is a key problem in various fields ranging from erosion of material, ignition of explosive, to sonoluminescence, etc. We study such processes using the material-point-method developed recently in the field of solid physics. The main points of the research include the relations between symmetry of collapsing and the strength of shock, other coexisting interfaces, as well as hydrodynamic and thermal-dynamic behaviors ignored by the pure fluid models. In the case with strong shock, we study the procedure of jet creation in the cavity; in the case with weak shock, we found that the cavity can not be collapsed completely by the shock and the cavity may collapse in a nearly isotropic way. The history of collapsing significantly influences the distribution of hot spots in the shocked material. The change in symmetry of collapsing is investigated. Since we use the Mie-Gr% {u}neisen equation of state and the effects of strain rate are not taken into account, the behavior is the same if one magnifies the spatial and temporal scales in the same way.
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