Abstract: To determine the target resistance of concrete materials, the constitutive description of concrete materials idealizes the pressure -volumetric strain as tri-linear equations of state, and the shear strength-pressure as Mohr-Coulomb with tension cutoff and shear saturation. The response of semi-infinite concrete target under high velocity impact is divided into four zones of elastic, cracked, compacted and condensed. The quasi-static spherical expansion theory is developed, target resistance in A-T model is determined, and the penetration depth of semi-infinite concrete targets penetrated by high velocity long rod projectiles is analyzed. The analytic result of penetration depth is in good agreement with experiment data.