The author has recently been involved in the analysis of the seismic performance of several standard types of cryogenic pressure vessel which were originally designed in the United States. Particular attention was accorded to the magnitude and distribution of the localised membrane and bending stresses developed in the inner and outer vessels near the points at which the internal and external support systems are attached. The analyses revealed that reinforcement would be required in certain critical areas in order to meet the design rules established by the relevant New Zealand government agency. Suitable modifications were made in these areas, although there seems reason to believe that the design rules may in some respects be unduly conservative.