Tropical cyclones are one of the nature’s most violent manifestations and potentially the deadliest of all meteorological phenomena. The casualty associated with major cyclones in the Indian sub-continent in the recent past give an idea about its enormous destructive capability. Purpose of the present paper is to identify the months of maximum possibility of occurrence of severe tropical cyclones over Bay of Bengal and Arabian Sea. The methodology adopted in this study is based upon the process of “Statistical Hypothesis Testing”. The statistical procedure is applied to fit a Poisson distribution to the monthly frequency distribution of occurrence of severe tropical cyclones over the coasts of Bay of Bengal and Arabian Sea. It is observed that Poisson distribution is a good fit to the monthly frequency distribution of severe tropical cyclones over Bay of Bengal and Arabian Sea. The concept of Shannon entropy is then applied to distinguish the months in accordance with the measure of vulnerability. It is identified that the month of May in the pre-monsoon season and the months of October and November in the post-monsoon season are highly susceptible for the occurrence of severe tropical cyclones over Bay of Bengal and Arabian Sea.