Eurypterids (sea scorpions) are extinct aquatic chelicerates. Within this group, members of Pterygotidae represent some of the largest known marine arthropods. Representatives of this family all have hypertrophied, anteriorly-directed chelicerae and are commonly considered Silurian and Devonian apex predators. Despite a long history of research interest in these appendages, pterygotids have been subject to limited biomechanical investigation. Here, we present finite element analysis (FEA) models of four different pterygotid chelicerae-those of Acutiramus bohemicus, Erettopterus bilobus, Jaekelopterus rhenaniae, and Pterygotus anglicus-informed through muscle data and finite element models (FEMs) of chelae from 16 extant scorpion taxa. We find that Er. bilobus and Pt. anglicus have comparable stress patterns to modern scorpions, suggesting a generalised diet that probably included other eurypterids and, in the Devonian species, armoured fishes, as indicated by co-occurring fauna. Acutiramus bohemicus is markedly different, with the stress being concentrated in the proximal free ramus and the serrated denticles. This indicates a morphology better suited for targeting softer prey. Jaekelopterus rhenaniae exhibits much lower stress across the entire model. This, combined with an extremely large body size, suggests that the species likely fed on larger and harder prey, including heavily armoured fishes. The range of cheliceral morphologies and stress patterns within Pterygotidae demonstrate that members of this family had variable diets, with only the most derived species likely to feed on armoured prey, such as placoderms. Indeed, increased sizes of these forms throughout the mid-Palaeozoic may represent an 'arms race' between eurypterids and armoured fishes, with Devonian pterygotids adapting to the rapid diversification of placoderms.