In this contribution, the mechanical properties of polyester cords are investigated in a series of experiments: monotonic, multistep relaxation, and cyclic loading-unloading tests. The nonlinear elastic behavior due to crimping of the fibers and the inelastic behavior appear in the test results. To represent this behavior, a constitutive material model is proposed by decomposing it into endochronic, viscoelastic, strain-hardening, stretch-induced stiffening, and matrix parts. The identified material parameters capture the experiments qualitatively well. The proposed model is validated with the additional experiments including the complex conditions and further evaluated through finite element simulations of the tire building process.