Abstract: Ultra-high-performance concrete (UHPC) is a new type of cemetitious composite material with ultra-high strength, ultra-high durability and high toughness. It has received extensive attention in the field of civil engineering at home and broad because of its superior performance and had a broad prospect of engineering application. The uniaxial tensile and compressive stress-strain constitutive model is the premise and foundation for the analysis of mechanical properties of UHPC members. In order to further study mechanical properties of UHPC, this paper summarized different UHPC constitutive models proposed by domestic and foreign scholars, including uniaxial compressive stress-strain relationship, uniaxial tensile stress-strain and stress-crack width relationship, and carries on the classification and comparison. Some similarities and differences of existing models are found, and the reasons for this difference were analyzed. In the last part, some constitutive relations were applied to the finite element analysis software ABAQUS. Numerical simulation of UHPC beam reinforced with high strength steel bars was carried out, and the rationality of some constitutive models was verified by comparison with the experimental results. Some conclusions were put forward. The research results of this paper provide a basis for structural performance study, structural analysis and structural design of UHPC.