When pipe flange connections clamped with sheet gaskets are subjected to thermal load, the bolt preloads that tighten a pair of pipe flanges tend to decrease. It has been studied in the previous paper why and how the bolt preloads decrease, in which the loading and unloading curves of sheet gaskets at elevated temperature are expressed by simple equations. Meanwhile, it is also known that the bolt preloads are likely to decrease when the plant is shut down. In this paper, a numerical procedure, which can estimate the amounts of bolt preload reduction occurred in the shutdown process, is proposed using axi-symmetric FEM. The analytical objects are pipe flange connections tightened with aramid sheet gaskets. In the finite element formulation, the stress-strain curves of the gaskets after plant shutdown are approximated by simple curves, considering that the hysteresis appeared in the curves is fairly small comparing to the loading and unloading curves. It is shown that the bolt preloads decrease as much as 50% of those in the running condition. The validity of the proposed numerical method is confirmed by comparing the numerical results of bolt preload reduction to experimental ones.