A combined numerical and analytical study of penetration of concrete by high velocity (approx. 1.8 km/s) projectiles was conducted. The effects of concrete's constitutive modeling on penetration calculations were studied and are discussed. The results of the analysis are compared with the available experimental data. All constitutive models studied accounted for the compressibility of concrete. The plastic yield condition was modeled with the von Mises yielding criterion using: (1) constant yield-strength model and (2) pressure-dependent yield-strength model. Regardless of the value of the yield strength, application of a constant yield strength model resulted in nearly identical hole profiles which, in all cases, significantly disagreed with the experimental data. Crater profiles calculated with the pressure-dependent yield model showed good agreement with the available experimental data. The reduction in the calculated crater profiles was attributed to the increased target resistance to penetration. A detailed analysis of the flow field along the central streamline shows that increases in the target's resistance to penetration are due to the growth in the time rate of the projectile erosion.