Abstract:The fundamental problems of near cavity of penetration and explosion in rock are discussed;and some development tendencies are presented. The expressions about the kinematics problems near cavity do not agree well with the stress and the deformation states. That are the reasons that considerable errors exist in the results of many scholars studies. According to the stress and deformation states near cavity in practice,the relation formulas for the kinematics of medium are deduced by using the laws of conservations of momentum and mass;and the problem of the speed of the deformation wave is solved. With the proposed relation formulae,some useful results such as the proportional conversion relation of penetration and impenetration,geometrical resemblance relation of explosion near cavity,can be clearly understood. The application results of case study show that the proposed relation formulas are practical.