The aim of model-based structural identification is to make sense of monitoring data in order to improve knowledge of the real behaviour of structures. Common use of structural-identification techniques involves an assumption of independent zero-mean Gaussian uncertainty at all measurement locations. However, when evaluating complex civil structures, this assumption is rarely correct. This study presents examples of common sources and forms of modelling uncertainties arising from modelling assumptions that are made when evaluating complex civil structures. A case study, the structural identification of the International Bridge in New Jersey, illustrates for each uncertainty source, likely forms of the probability-density function based on engineering judgment. This study demonstrates that most sources of modelling error cannot be estimated by independent Gaussian uncertainty. In addition, the number of uncertainty sources is usually not large enough to satisfy the central-limit theorem when they are combined.