The viscoelastic behavior of a plain-woven polyester fabric is studied. The viscoelastic properties of the woven fabric are determined via creep and stress relaxation tests. A rheological model of the woven fabric is proposed. The model consists of six simplest elements, including three linearly elastic, two linearly viscous, one dry friction element, and two elements with more complex properties, namely, a hysteretic element and a nonlinearly elastic element. This model describes the elastic, plastic, viscoelastic, and hysteretic properties of the fabric at room temperature in the range of strain rates from 0.001 to 10 min(-1). Additional validation tests are also carried out, including creep and creep recovery, stress relaxation, inverse stress relaxation, and cyclic loading and unloading tests. The process duration and stress level are also varied. The predictive quality of the proposed rheological model is shown.