The long term tightness performance of stuffing-box packings, used in valves, is conditioned by the capacity of its sealing material to maintain a contact pressure to a predetermined minimal threshold value. Due to the creep, this contact pressure decreases with time depending on the creep properties and the stiffness of the housing. Assessing relaxation is a key parameter in determining the tightness performance of a valve stem packing over time. An analytical model based on the packing viscoelastic behavior is developed to assess the contact pressures between the packing material and the stem and the housing and their variation with time. In parallel, an axisymmetric 2D finite element model was build to validate and support the analytical model. The valve stem packing relaxation performance is an important design parameter to consider when selecting compression packings.