The tightness of valves, compressors and pumps is ensured by superposed braided rings installed in a stuffing-box system. The nature of the packing material and structure, which is like a rectangular braided cord, influences the proper stuffing-box assembly behavior. During installation, a minimum compressive load is required to ensure a minimum level of tightness. A fairly large percentage of this axial compression load is transferred to the radial direction to generate the contact pressures at the packing-stem and packing-housing interfaces necessary for sealing.The packing is considered in several studies as a viscoelastic material with its creep-relaxation behavior assumed as one-dimensional rheological model. In the present work, relaxation tests in a test-bunch containing all the components of the packed stuffing-box, are carried out to define a creep constitutive law for packing braids of different materials. Based on three-dimensional compression tests the developed method is applied to three different packing materials.