Steel fiber has become a reinforcing material with increasing application demand in civil engineering, so the damage and fracture of steel fiber reinforced concrete (SFRC) is also a key problem that needs to be solved urgently in engineering. Based on the unified phase field theory and cohesion model proposed recently, a meso-finite element model of SFRC composed of steel fiber, aggregate, mortar and interface transition zone was established and verified by experiments. Under the conditions of uniaxial tension and three-point bending, the effects of factors such as steel fiber content and length, aggregate shape, and initial notch defects on the tensile and flexural properties of SFRC were investigated, and the mechanical properties and damage mechanism of SFRC were studied. The results show that the SFRC meso-finite element model based on the phase field damage model and cohesion model has good accuracy and reliability. The tensile strength of SFRC is greatly affected by the content of steel fiber, and the cost performance is higher at 2% content, which is 34.2% higher than that at 0.5% content. The influence of aggregate shape and steel fiber length is small. The bending strength of SFRC is greatly affected by the content of steel fiber and the cut depth. The addition of 0.2%, 0.35% and 0.5% steel fiber increase the bearing capacity of SFRC cut beam by 20.7%, 38.9% and 63.7%, respectively, compared with SFRC cut beam with a cut depth of 25 mm. The bearing capacity of SFRC beam with 40 mm and 55 mm incision depth decrease by 19.9% and 39.8%, respectively. It can be used as reference for steel fiber reinforced concrete engineering analysis and design.