Objectives  The formulation of the second generation intact stability criterion by IMO is in the stage of continuous improvement. As the first and second level vulnerability assessment methods of dead ship stability are based on different principles, the inconsistency of evaluation results is obvious, so that the accuracy of the assessment methods needs to be further discussed and analyzed.

  Methods  Rolling period is the main factor affecting the evaluation results. Firstly, based on the differential equation of ship motion, the problems using the existing rolling period calculation method to evaluate were analyzed and discussed; secondly, the calculation method of rolling period in SDC 5/6/8 was applied to the first level vulnerability criteria of dead ship stability, the corresponding program was written as well; 24 sample ships including 72 loading conditions were selected to compare and analyze the calculation results by using the existing and modified method.

  Results  The results show that, for the ships with obvious non-linear characteristics, more accurate results can be obtained by using the rolling period calculation method to evaluate the vulnerability.

  Conclusions  It is suggested to evaluate the weakness and formulate the subsequent operation limitation with the calculation method of non-linearity-based rolling period.