Abstract: Considering the effects of coating, and the effects of tensile time, tensile rate, viscoelastic stress and reaction force on initial stress, the improved hyperelastic constitutive and viscoelastic constitutive model of thermoplastic polyurethane composite fabric and a single fiber bundle were established by tensile test. The stress-strain and stress relaxation curves during the tensile process were predicted and compared with the test results. The results show that the established hyperelastic constitive model could accurately predict the stress-strain curve of the fabric and the single fiber bundle, and the realtive errors were less than 3.5%. The viscoelastic constitutive model could accurately predict the stress relaxation curve of the fabric, and the relative error was less than 3.21%.