A dynamic constitutive damage model for reinforced concrete (RC) structures and formulations of blast loading for contact or near-contact charges are considered and adapted from literatures. The model and the formulations are applied to the input parameters needed in commercial finite element method (FEM) codes which is validated by the laboratory blast tests of RC slabs from literature. The results indicate that the dynamic constitutive damage model based on the damage mechanics and the blast loading formulations work well. The framework on the dynamic constitutive damage model and the blast loading equations can therefore be used for the simulation of failure of bridge components in engineering applications.