Crosslinking mass spectrometry is increasingly used for structural characterization of multisubunit protein complexes. Chemical crosslinking captures conformational heterogeneity, which typically results in conflicting crosslinks that cannot be satisfied in a single model, making detailed modeling a challenging task. Here we introduce an automated modeling method dedicated to large protein assemblies ('XL-MOD' software is available at http://aria.pasteur.fr/supplementary-data/x-links) that (i) uses a form of spatial restraints that realistically reflects the distribution of experimentally observed crosslinked distances; (ii) automatically deals with ambiguous and/or conflicting crosslinks and identifies alternative conformations within a Bayesian framework; and (iii) allows subunit structures to be flexible during conformational sampling. We demonstrate our method by testing it on known structures and available crosslinking data. We also crosslinked and modeled the 17-subunit yeast RNA polymerase III at atomic resolution; the resulting model agrees remarkably well with recently published cryoelectron microscopy structures and provides additional insights into the polymerase structure.