Given the inherent uncertainty in estimates produced by decision analytic models, the assessment of uncertainty in model-based evaluations is an essential part of the decision-making process. Although the impact of uncertainty around the choice of model structure and making incorrect structural assumptions on model predictions is noted, relatively little attention has been paid to characterising this type of uncertainty in guidelines developed by national funding bodies such as the Australian Pharmaceutical Benefits Advisory Committee (PBAC). The absence of a detailed description and evaluation of structural uncertainty can add further uncertainty to the decision-making process, with potential impact on the quality of funding decisions. This paper provides a summary of key elements of structural uncertainty describing why it matters and how it could be characterised. Five alternative approaches to characterising structural uncertainty are discussed, including scenario analysis, model selection, model averaging, parameterization and discrepancy. We argue that the potential effect of structural uncertainty on model predictions should be considered in submissions to national funding bodies; however, the characterisation of structural uncertainty is not well defined within the guidelines of these bodies. There has been little consideration of the forms of structural sensitivity analysis that might best inform applied decision-making processes, and empirical research in this area is required.