A strain rate dependent orthotropic model for steel fiber reinforced concrete (SFRC) structures subjected to impact or blast loads is proposed in this paper. Based on the previously introduced orthotropic model for plain concrete, an improved strain rate dependent material model for SFRC is developed to account for the effect derived from the addition of steel fibers in the concrete matrix and to cope with the multiaxial strain rate dependent behavior of SFRC. In addition to verification of the constructed multiaxial strength envelope of SFRC through correlations with experimental data, improved failure strains in the uniaxial stress-strain relation are also introduced to minimize the mesh size dependency in the numerical results. Finally, the proposed orthotropic model is incorporated into LS-DYNA as a user defined material model. Numerical analyses were performed for experiments of RC and SFRC slabs under projectile impact and blast loading, and the obtained results show that the addition of the steel fibers provides a considerable improvement in the structural resistance and the proposed model effectively simulates the structural responses of SFRC structures while minimizing the mesh size dependency in the numerical results.