Modern software architectures such as microservices provide a high degree of scalability, changeability, and maintainability in application development. Furthermore, enabling controlled failure of microservices can provide abstract‐level solutions to design more resilient applications. In this paper, we introduce modularity vulnerability to analyze the vulnerability of a modular software design model under the failure of m top‐rank modules by the proposed structural metrics. The study analyzes the modularity quality coefficient (MQC) under the failure of the critical modules identified using the proposed parameter‐based greedy strategy. We conduct a comprehensive analysis of the software design generated by well‐known models and online datasets and provide a perspective for reasoning about the correlation between modularity metrics. The results show that the failure of the modules with the highest cluster factor (CF) value leads to a maximum decrease in the software modularity quality. Finally, we show a linear correlation between CF and the variations of the MQC, implying stability in the software modularity analysis (SMA) problem.