Abstract: The problem about a projectile with high velocity impactingon a target is an important subject in weapon-design. In this paper, the conservation laws and the constitutive equations, are formulatedfor Lagrange finite element method. 4-node two-dimensional isoparametricelement are used for the spatial discretization. The explicit central difference method is used for integrating with respect to time. Anti-hourglassnode forces are introduced for controlling hourglass modes in the computation of large elastic plastic deformation. Wilkins' sliding surfaces technique is used for impact interface. The results show that the finite element numerical analysis is one of the effective methods in field of the high velocity impact.