This paper presents a computational study on the flexural fracture behaviors of steel fiber reinforced concrete (SFRC). The focus is on investigating the impacts of various factors on SFRC, utilizing a discrete-continuum coupled finite element method. This method explicitly models each material phase, including coarse aggregates, mortar paste, steel fibers and interfacial transition zones (ITZs), allowing precise tracking of mesoscale cracking during bending. The simulation method is developed, calibrated and validated before conducting a parametric investigation. Critical factors considered include the spatial positioning of coarse aggregates and steel fibers, fiber content, length and diameter, and the bonding property of fiber-mortar ITZs. Results indicate that steel fibers modify crack development in notched beams, causing greater distortion in the primary crack. Increasing fiber content from 0 to 2% enhances flexural tensile strength but introduces more variability. Longer fibers initially increase strength, then decrease, while thicker fibers consistently reduce strength. Improving the bond between fibers and mortar does not substantially increase the load-bearing capacity of the beam. In conclusion, this study shows how the established approach enhances understanding of the mechanical responses of SFRC under flexural-fracture loading.