This thesis investigates the behavior of normal and steel fiber reinforced concrete (SFRC) under quasi-static and dynamic loading. The focus of the thesis is on the investigations under dynamic loading. Previous research has shown that the addition of steel fibers can significantly improve many of the desired technical properties of hardened concrete, such as fracture toughness, flexural strength, fatigue strength, thermal shock resistance and cracking. In this context, many experimental and numerical studies indicate that the strength of such composites is rate-dependent, i.e. it is strongly influenced by increasing the dynamic load. This effect applies both to the composite components concrete and steel fibers and to the composite interaction between them. The phenomenon is generally known as the strain rate effect. In this research work, numerical investigations were carried out to systematically analyze the influence of the addition of steel fibers to the concrete matrix and to investigate the dependence of this material on the strain rate. Three numerical studies were carried out. In the first study, the bond behavior between steel fiber and the adjacent concrete matrix was investigated using different approaches with the finite element software LS-DYNA. The results were compared with available experimental data. In the second study, the behavior of unreinforced and steel fiber reinforced concrete slabs under impact loading was investigated. The models were developed and calibrated. The quality and reliability of the models were evaluated in a series of numerical case studies. The calculated results were verified by comparison with the available experimental data. The dynamic behavior of unreinforced concrete and fiber-reinforced concrete was investigated in the third study, examining both compressive and tensile behavior. These studies aimed to investigate the contribution of the steel fibers to the global strength or resistance behavior of unreinforced and fiber-reinforced material under dynamic loading, with little attention paid to the influence of the steel fibers on the cracking of the fiber-reinforced concrete. In addition, the contribution of the material effect and its ability to capture the dynamic behavior of plain and fiber-reinforced concrete are of interest. The focus here is on the proposed material model for the concrete. It is shown that the proposed concrete model can reproduce the compressive and tensile dynamic behavior of unreinforced and fiber-reinforced concrete well and can realistically predict the experimental results. Finally, numerical case studies on the dependence of the results on mesh size, fiber content, fiber length-to-diameter ratio, concrete strength and loading rate followed. The parameters with the greatest influence were identified and analyzed, and a conclusion was drawn. It was shown that the aforementioned parameters are actively involved in the overall behavior of the materials and can play a significant role in this.