Abstract: The flexure-shear and direct shear failure modes of RC structures due to blast loading are possibly observed experimentally apart from the frequently observed flexural failure mode. Much attention has been paid to this aspect, especially the exact prediction of the dynamic response and failure modes of RC structures due to blast loading. Some recent progress relevant to the following aspects is presented: (1) a 2D elasto-viscoplastic finite element method for concrete structures is developed by extending the proposed strain rate-sensitive material model to the constitutive relationship of concrete under two-dimensional state; (2) based on the theory of Timoshenko beam and theory of elasto-viscoplasticity, a finite element method and a finite differential method are proposed respectively to predict the dynamic response and failure modes of shallow-buried RC structures. It is demonstrated that the proposed 2D elasto-viscoplastic finite element method can predict the flexural failure modes of blast-loaded RC structures, and the proposed Timoshenko beam finite element method and finite differential method can determine the flexural, flexure-shear and direct shear failure modes of blast-loaded RC structures.