To identify the sensitive factors in mechanical safety of explosion vessels, a parameter sensitivity analysis model based on the Latin Hypercube Sampling (LHS) and the Spearman partial rank correlation analysis methods is built. A great number of numerical simulations and statistical analyses were carried out for the explosion process in a hermetic vessel with this model, the sensitivity values and the orders of related factors were obtained, the impacts of the sample sizes, the parameter distribution types and the parameter value ranges on the sensitivity results were analyzed, and a comparison between the method in this paper and other sensitivity analysis methods was made. It is shown that the volumetric internal energy and the yield strength are the most sensitive factors in mechanical safety of the sample vessel, the tangent modulus is a relatively sensitive factor, while the elastic modulus and the Poisson's ratio are insensitive factors. It is also shown that the volumetric internal energy has a positive correlation with the vessel strain, the Poisson's ratio has no correlation with the vessel strain, while other factors have negative correlations with the vessel strain. The sensitivity analysis method presented in this paper can be used for the sensitivity analysis of various explosion vessels, to provide a quantitative basis for optimizing the vessel safety design and to enhance the safety in tests.