Bolted flange joints are part of pressure vessel and piping components and are extensively used in the chemical, petrochemical, and nuclear power industries. They are simple structures and offer the possibility of disassembly, which makes them attractive to connect pressurized equipment and piping. In addition to being prone to leakage, they often require maintenance while in operation in which case the bolts are either retightened as in hot torquing or untightened to be replaced. Although costly shutdowns are avoided, such maintenance work exposes the operator to a potential risk because the bolt load alteration can produce a gasket load unbalance, which results in the local gasket contact stress to drop below some critical value, causing major leak and hence jeopardizing the life of the worker. This paper addresses the issue of the contact stress level unbalance around the flange when the bolts are subjected to initial tightening. The study compares the contact stress distribution variations, an analytical developed model based on the theory of rings on elastic foundation, to those given by the finite element model and the simple beam on elastic foundation model developed by Koves (2007, “Flange Joint Bolt Spacing Requirements,” Proceedings of PVP2007, ASME Pressure Vessel and Piping Division Conference). This study is developed for the purpose of helping limit the degree of load increase in hot torquing or the maximum number of bolts to be replaced at a time and identify those flanges for which the bolt cannot be replaced in service.