In the present paper, a concrete material is taken as a studying object, both the No. 16 and the JHC constitutive models in LS-DYNA commercial software are used because the parameters of both models are comparatively easy to obtain. The results show that, computational maximum value and the width of the overload curves are good agreement with experimental curves by using these two models in the Lagrange method. With increasing penetrating depth, the ramp and down slopes of the overload curves by computing is increasingly agreement with experimental curves. The JHC model is better to compute overload curves in the Lagrange method. The Lagrange method is also used to compute the penetration of multilayer concrete plate. It is found that, the peak value of acceleration goes down with increasing penetrating layers; this decreasing peak value depends on layer thickness and the strength. Acceleration value between layers will go to zero; this trend is agreement with experiments.