To investigate the mechanical response and fracture mechanism of the steel fiber reinforced concrete (SFRC) structure, a numerical modeling method based on the application of cohesive elements was proposed. In the proposed model, cohesive elements were used to characterize the potential fracture surfaces and the rebar-concrete interfaces. By considering the mixed-mode damage relation, friction, and the bridging effect of fibers, a constitutive model of SFRC potential fracture surfaces was developed. Besides, based on the traditional bond-slip relation, a modified constitutive model of the rebar-concrete interface was proposed by considering the separation in the normal direction. To validate the proposed model, a group of SFRC four-point bending experiments was carried out. Through the comparison between the simulation and experiments, the proposed model was proved to be able to simulate the mechanical response and the fracture behavior of the SFRC structure appropriately. According to the characterization of the SFRC constitutive model, the influence of the fiber content and concrete friction factor on the structure bearing capacity was studied. It is found that when the fiber content is small or the friction factor is unreasonable, the bearing capacity and the ductility would decrease significantly.