Cycle analysis has been performed to find out the optimum design point of the BOG re-liquefaction plant. The cycle state, defined by three cycle variables, was mainly described by the three cold temperatures of the three-pass heat exchanger, on which the constraints by the heat exchanger are imposed. The cycle states which are confined within a domain limited by the temperature constraints were the primary issue of this study. The BOG mass within the domain was analyzed first and then the cycle performance was related to the BOG mass afterwards, which enabled us to explain the observed behavior of the cycle performance under the temperature constraints by the heat exchanger. A good cycle performance could be ensured if the two cold Nitrogen temperatures of the three temperatures were placed close together near -140℃ while the BOG temperature is kept far above enough, but not too far, fr