The steel plate reinforced concrete (SC) walls and roofs are effective protective structures in nuclear power plants against aircraft attacks. The mechanical behavior of the concrete in SC panels is very complicated when SC panels are under the action of impacting loading. This paper presents a dynamic material model for concrete subjected to high-velocity impact, in which pressure hardening, strain rate effect, plastic damage, and tensile failure are taken into account. The loading surface of the concrete undergoing plastic deformation is defined based on the extended Drucker–Prager strength criterion and the Johnson–Cook material model. The associated plastic flow rule is utilized to evaluate plastic strains. Two damage parameters are introduced to characterize, respectively, the plastic damage and tensile failure of concrete. The proposed concrete model is implemented into the transient nonlinear dynamic analysis code ls-dyna. The reliability and accuracy of the present concrete material model are verified by the numerical simulations of standard compression and tension tests with different confining pressures and strain rates. The numerical simulation of the impact test of a 1/7.5-scale model of an aircraft penetrating into a half steel plate reinforced concrete (HSC) panel is carried out by using ls-dyna with the present concrete model. The resulting damage pattern of concrete slab and the predicted deformation of steel plate in the HSC panel are in good agreement with the experimental results. The numerical results illustrate that the proposed concrete model is capable of properly charactering the tensile damage and failure of concrete.