Abstract: The direct tensile tests under monotonic and cyclic loading were conducted on the ultra high performance concrete (UHPC) with different tensile strain characteristics (strain hardening and strain softening). The test results reflect that the strain hardening UHPC enters the stage of strain hardening with multi-point microcrack distribution after the cracking of UHPC matrix, and it enters the strain softening section with single seam cracking after reaching the ultimate tensile strength. The strain softening UHPC enters the strain softening stage with single seam crack after the cracking of UHPC matrix. The envelope of axial tensile stress-strain curves of the two types UHPC under cyclic load are generally consistent with that curves under monotonic load. Based on the stiffness degradation process, the axial tensile damage evolution equations of two types of UHPC were established. Based on the measured stress-strain curves and the crack distribution of the specimens, the axial tensile constitutive relation models of the two UHPCs were established. The test data are satisfactorily approximate to the proposed models. The equivalent method for the strain hardening UHPC with two-stage axial tensile constitutive relation in numerical calculation was studied by using energy method. Finally, the proposed axial tensile constitutive relation model and damage evolution equation of strain hardening UHPC were verified according to the numerical simulation of unreinforced strain strengthened UHPC flexural test beam. The results reveal that the proposed axial tensile constitutive model could precisely predict the ultimate bearing capacity of UHPC flexural-tensile members, and the axial tensile damage variables could generally reflect the crack distribution of the specimens.