AbstractIncremental dynamic analysis (IDA) has been extended by introducing a set of structural models in addition to the set of ground motion records which is employed in IDA analysis in order to capture record‐to‐record variability. The set of structural models reflects epistemic (modeling) uncertainties, and is determined by utilizing the latin hypercube sampling (LHS) method. The effects of both aleatory and epistemic uncertainty on seismic response parameters are therefore considered in extended IDA analysis. The proposed method has been applied to an example of the four‐storey‐reinforced concrete frame, for which pseudo‐dynamic tests were performed at the ELSA Laboratory, Ispra. The influence of epistemic uncertainty on the seismic response parameters is presented in terms of summarized IDA curves and dispersion measures. The results of extended IDA analysis are compared with the results of IDA analysis, and the sensitivity of the seismic response parameters to the input random variable using the LHS method is discussed. It is shown that epistemic uncertainty does not have significant influence on the seismic response parameters in the range far from collapse, but could have a significant influence on collapse capacity. Copyright © 2008 John Wiley & Sons, Ltd.