This thesis proposes a Bayesian Influence Diagram (BID) based methodology to construct decision-aiding models to support political-strategic crisis decision making (PSCDM). The key methodological challenges are to adapt a quantitative modelling approach to this time-constrained and subjective process; to construct a general methodology that could be applied to future situations; to overcome the problem of limited access to subject matter experts for model building and validation; to enable elite experts to participate effectively in the largely technical and burdensome process of data elicitation; and to develop an effective and useful model that could complement existing decision processes and support rapid comparison and exploration of options. The methodology is designed around a multidisciplinary review of the literature on the fundamentals of human model-use, decision making under uncertainty, the construction and validation of decision-aiding models across multiple disciplines including operations research, decision support systems and Bayesian networks. From this review a BID based methodology was developed and demonstrated through a case study that focused on Australian Post-Cold War PSCDM. A model was successfully constructed and validated using qualified academics and experts and then applied to a synthetic, but historically-guided, decision situation. A data elicitation framework is proposed and demonstrated, including the use of an interview-ready model that reduces the elicitation burden on interviewees and helps senior decision makers to engage effectively in the elicitation process. Additionally this thesis proposes and demonstrates an integrated model building and validation framework tailored for PSCDM. The demonstration of the methodology in the Australian PSCDM case study identifies improvements for the methodology and areas for future research. Improvements include considering alternate independence of causal influence models within the Bayesian network structure to more effectively reduce the elicitation burden and to provide additional politically focused output measures from the model in addition to National Security Interest. Further research is recommended into the potential of increased automation of the textual analytics aspects of the methodology; the application of network analysis to gain early insight into potentially influential nodes; and to investigate the limits within which PSCDM can be assumed to be ergodic.