In case the systems have radioactivity, toxic liquid or expensive fluid, and have to be performed repair work at one point of the system pipe, the formation of an internal ice plug by the removal of heat from the pipe is often consideredas a useful method. In this procedure, an annular jacket is placed around the pipe, and the jacket is then filled with liquid Nitrogen(-196.deg. C). Thermal analysis by the finite element method based on the laboratory experiments has been constructed. The result of the finite element analysis on the experimental model shows to be reasonable, and thus the finite element analysis for different pipe size, material and thickness has been performed to see if the ice plugging procedure in various applications can be safely performed without possibility of damage to the pipe. It has been confirmed that in carbon steel pipes the maximum stress is found around the boundary of the freezing jacket, and the stress increases as pipe thickness increases, but the maximum stress shows no consistency along the increment of the pipe diameter. The maximum stresses appear lower than yield stress in carbon steel. It has been also shown that in stainless steel pipes the maximum stresses are also found around the boundary of the freezing jacket, but almost the same value in spite of different pipe size an thickness, and the maximum stresses show slightly higher than the yield stress of the stainless steel.