Summary Robust estimation of collapse risk should consider the uncertainty in modeling of structures as well as variability in earthquake ground motions. In this paper, we illustrate incorporation of the uncertainty in structural model parameters in nonlinear dynamic analyses to probabilistically assess story drifts and collapse risk of buildings. Monte Carlo simulations with Latin hypercube sampling are performed on ductile and non‐ductile reinforced concrete building archetypes to quantify the influence of modeling uncertainties and how it is affected by the ductility and collapse modes of the structures. Inclusion of modeling uncertainty is shown to increase the mean annual frequency of collapse by approximately 1.8 times, as compared with analyses neglecting modeling uncertainty, for a high‐seismic site. Modeling uncertainty has a smaller effect on drift demands at levels usually considered in building codes; for the same buildings, modeling uncertainty increases the mean annual frequency of exceeding story drift ratios of 0.03 by 1.2 times. A novel method is introduced to relate drift demands at maximum considered earthquake intensities to collapse safety through a joint distribution of deformation demand and capacity. This framework enables linking seismic performance goals specified in building codes to drift limits and other acceptance criteria. The distributions of drift demand at maximum considered earthquake and capacity of selected archetype structures enable comparisons with the proposed seismic criteria for the next edition (2016) of ASCE 7. Subject to the scope of our study, the proposed drift limits are found to be unconservative, relative to the target collapse safety in ASCE 7. Copyright © 2016 John Wiley & Sons, Ltd.

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