In order to solve the shortcomings of fragility analysis by finite element method, this paper proposes a method for calculating the structural fragility of nuclear containment under the loading of inner pressure (which is abbreviated as "inner pressure fragility") based on a simplified calculation method and related program (coded by Python) named as NCMC. This enables direct preliminary screening to delete unsuitable nuclear containment types that cannot meet the required failure probability. In addition, this paper conducts a detailed parameter analysis on factors such as concrete thickness and material type, liner thickness, and the numbers of tendons and rebars in the hoop and vertical directions. By analyzing the changes in failure probability due to parameter changes, based on confirming the safety margin and load bearing capacity of the original nuclear containment type, suggestions for parameter choices are provided for a certain containment. The same method and analyzing routine can also be used for realizing fast parameter selection for other structures.