The mathematical model of deformation and failure of rock (concrete) is presented based on the phenomena that projectile penetrates into rock (concrete)
considering the compressibility of the target material. The resistance of projectile in the process of penetration has been obtained. The motion equation of projectile is gained according to the Newton’s law of motion. The parameters and penetration depth of penetration are obtained; the equation is solved by using increment method. By comparing the result of calculation with ones from the empirical formulas
the practicability and reliability of the method are proved.