An orthotropic material model to predict the behavior of concrete subjected to dynamic biaxial or tri-axial loading is introduced in this paper. The proposed model is based on the dynamic triaxial strength envelope and the dynamic increase factor (DIF) obtained from multi-axial dynamic experiments for concrete. Differently from the plasticity based models, an orthotropic material model, which is one of the elasticity based models, can easily be implemented in numerical formulations because the stress state is directly determined from the defined stress-strain relation. In advance, consideration of the mesh-dependency in a finite element (FE) analysis is included in the model to accurately describe the failure process of concrete structures. The strength envelope and stress-strain curves of the proposed orthotropic model were compared with the available experimental data under multi-axial stresses, and then numerical analyses were performed for a perforation test of a concrete slab subjected to a projectile and a blast test of concrete beam. The results show that the proposed orthotropic model can effectively be used in the impact and blast analyses of concrete structures and gives numerical results that are insensitive to the employed FE mesh size. (C) 2017 Elsevier Ltd. All rights reserved.