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The stress-strain behaviour of woven and coated technical textiles for structural purposes is well known to be anisotropic, nonlinear and viscoelastic. Tensile tests with cyclic loads on woven structural fabrics show a saturating behaviour regarding the stress-strain characteristics. Permanent strains are well known to be considerable, particularly in the first load cycles. However, the increase of permanent strains reduces in the following load cycles until only negligible additional permanent strains are observed. In common experimental test practice for structural fabrics, three to five load cycles are applied in total. Results show, that the saturation process may be considered progressed at that point, but not yet finished. In general, elastic material behaviour could be adopted for material modelling in the framework of a numerical analysis when the saturation is finished by an acceptable tolerance. The present paper investigates, whether and when the saturation process is completely finished for a woven glass fibre fabric. For this purpose a specific experimental protocol was developed where longitudinal and transverse strains are considered in uniaxial tensile tests with multiple load cycles. Furthermore, in order to reach beyond the state-of-the-art linear-elastic material model, a new nonlinear anisotropic hyperelastic material model formulated in a full three-dimensional continuum mechanics setup can be considered. That means, that a change in thickness due to axial loading may be taken into account. For this reason, a protocol was developed such that the thickness change is also measured in the saturation tests. The results from these investigations are presented and interpreted in the present paper.