Abstract: In this paper, the response of the spherical cavity expansion theory is used to analyze the penetration of the target under the impact of the missile, and a general form of the penetration similarity is established based on the dimension theory. The analysis of the existing experimental data of the projectile shows that the non-dimensional penetration depth curve is deflected and shifted for difierent penetration speeds. With the strain-rate efiect and the damage evolution of the material, the geometric similarity laws do not hold true for the brittle materials such as the concretes. It is necessary to introduce a correction of the geometric similarity law to account for the strain-rate efiect and the damage evolution of the material.