A tensile failure criterion that can minimize the mesh-dependency of simulation results on the basis of the fracture energy concept is introduced, and conventional plasticity based damage models for concrete such as CSC model and HJC model, which are generally used for the blast analyses of concrete structures, are compared with orthotropic model in blast test to verify the proposed criterion. The numerical prediction of the time-displacement relations in mid span of the beam during blast loading are compared with experimental results. Analytical results show that the numerical error is substantially reduced and the accuracy of numerical results is improved by applying a unique failure strain value determined according to the proposed criterion.