Concrete behaves often rather differently from most other construction materials in that its plasticity is highly dependent on the stress state. The strength differs significantly from the tensile state to the compression state, and the density changes under the applied load due to dilation as well as compaction of the porous content of the material. While these issues are rather cumbersome to solve based on the classical fracture mechanics method, it is realistic today to be accounted for according to the damage mechanics method, especially since the computational hardware and software have been evolved rapidly in the recent decades. Together with experimental investigations, a numerical tool and two material models for concrete have been studied in this work. The complex RHT (Riedel-Hiermaier- Thoma) and CSCM (continue surface cap method) concrete material models have been investigated for their capability to deal with cracking and damage evaluation issues in the reinforced concretes subjecting to high velocity impact and dynamic loading conditions. It has been demonstrated that by considering advanced material models, a reasonable estimation of the cracking and damaging process in the concrete material may be achieved. The advanced models accounts for non-homogeneous plasticity, the strength as a function of all the three stress invariants, as well as the fracture energy and strength as a function of the strain rate. However, the material model and the constitutive equation still need some improvements in the high strain rate regime.