The engineering analysis technique finite element analysis (FEA) is used here to investigate cranial stress and strain during biting and feeding in three phylogenetically disparate theropod taxa: Coelophysis bauri, Allosaurus fragilis and Tyrannosaurus rex. Stress patterns are generally similar in all taxa with the ventral region of the skull tensed whilst the dorsal aspect is compressed, although the skull is not purely behaving as a cantilever beam as there is no discernible neutral region of bending. Despite similarities, stress patterns are not wholly comparable: there are key differences in how certain regions of the skull contain stress, and it is possible to link such differences to cranial morphology. In particular, nasal morphology can be explained by the stress patterns revealed here. Tyrannosaurus models shear and compress mainly in the nasal region, in keeping with the indistinguishably fused and expanded morphology of the nasal bones. Conversely Allosaurus and Coelophysis models experience peak shear and compression in the fronto-parietal region (which is tightly interdigitated and thickened in the case of Allosaurus) yet in contrast the nasal region is lightly stressed, corresponding to relatively gracile nasals and a frequently patent internasal suture evident in Allosaurus. Such differences represent alternate mechanical specializations between taxa that may be controlled by functional, phylogenetic or mechanical constraints. Creation of finite element models placed in a phylogenetic context permits the investigation of the role of such mechanical character complexes in the cranium of nonavian theropods and the lineage leading towards modern birds. © 2005 The Linnean Society of London, Zoological Journal of the Linnean Society, 2005, 144, 309–316.