Similar to many polymer materials, high-density polyethylene (HDPE) and polyvinyl chloride (PVC) show a clear creep behavior, the rate of which is influenced by temperature, load, and time. Most bolted flange joints undergo relaxation under compression, which is caused by the creep of the material. However, the creep property of the two polymers is different under tension and compression loading. Since the sealing capacity of a flanged gasketed joint is impacted by the amount of relaxation that takes place, it is important to properly address and predict the relaxation behavior due to flange creep under compression and thereby reducing the chances of leakage failure of HDPE and PVC bolted flange joints. The main objective of this study is to analyze the compressive creep behavior of HDPE and PVC flanges under normal operating conditions. This is achieved by developing a respective creep model for the two materials, based on their short-term experimental creep test data. Both numerical and experimental simulations of the polymeric flange relaxation behavior are conducted on an NPS 3 class 150 bolted flange joint of dissimilar materials, where one of the flanges is made of HDPE or PVC material and the other one is made of steel SA105. The study also provides a clear picture on how the compression creep data of ring specimen may be utilized for predicating the flange bolt load relaxation over time at the operating temperatures.