This article considers the issue of uncertainty analysis in general and also its relevance to structural health monitoring. Brief descriptions of the most popular of the many frameworks for uncertainty representation are given. The three main uncertainty‐related problems of relevance to structural dynamics, namely, quantification, fusion, and propagation, are then discussed. In order to illustrate the preceding ideas in a realistic scenario, two case studies conducted on an aerospace structure, namely the wing of a Gnat trainer aircraft, are provided. The first case study considers the issue of attaining certification for the artificial neural network damage classifiers through the assessment of the network's robustness to uncertainty. This case study involves the propagation of intervals through the network structure and it was found that it is likely that the networks which would be considered as optimal, in the traditional sense, would not be the network that is most robust to uncertainty. The second case study considers evidence‐based classifiers as an alternative to probabilistic classifiers for the problem of damage location. The Dempster–Shafer theory is employed to construct neural network classifiers with the potential to admit ignorance, rather than misclassify. Issues of propagation and fusion in an evidence‐based framework are considered. It was also found that Dempster–Shafer networks give a slight improvement over their probabilistic counterparts.