Critical infrastructures vulnerability assessment involves understanding various socio-technological aspects of modern day infrastructures. While vulnerabilities exist at different scales, failures of large-scale installations in infrastructures are significant because they lead towards widespread social and economic disruptions. There is growing awareness of the multiple potential causes of failure, including those due to dependence upon other infrastructures. This paper establishes a framework for national analysis of vulnerability of interdependent infrastructures. We present: (i) A mathematical formulation of the vulnerability assessment; (ii) Network models for infrastructures that take in account the geographic, physical and operational characteristics of connecting nodes and edges; (iii) Interdependency mapping models that establish relationships between different subsystems within and across infrastructures; and (iv) Methods for implementing failure and disruption calculations. The methodology is demonstrated for Great Britain’s railway infrastructure, for which we have built detailed interdependency mappings between critical assets and infrastructures that support railway operations. Two key vulnerability assessment results, produced to examine failure impacts of such assets on railway passenger trip flows, include: (i) Random failure outcomes; and (ii) Flood vulnerability outcomes. The results show which critical infrastructure interdependencies potentially have large impacts on railway operations, providing a useful analysis tool for further risk and adaptation planning.