Archosaurs (crocodiles, birds and relatives) have included many locomotor habits throughout their history. They are notable in the repeated evolution of obligate bipedality – rarely achieved by other clades – with birds inheriting their bipedal stance from dinosaurs. Yet, owing to marked anatomical transformations, birds may not be suitable for interpreting locomotor function and evolution in all bipedal archosaur lineages. Computational musculoskeletal models and simulations of extinct species can provide an avenue to exploring these questions, using established biomechanical principles. Here, we used in silico predictive simulations to explore musculoskeletal function and performance using dynamic optimization; under the assumption that a behaviour maximizes some performance objective, this can generate simulations of behaviours de novo. We developed simulations of maximum speed running in the extinct dinosaur Coelophysis (~15 kg), as well as a modern ground bird, a tinamou (~600 g). Using a subject-specific musculoskeletal model of the tinamou, combined with a Hill-type muscle model, we generated simulations of walking and running gait that were comparable to prior empirical data, and a maximum speed of 3.45 m/s was predicted. Given that soft tissues are not preserved in the fossil record, we also identified the requirements for a simple muscle model (ignoring force–length–velocity effects) that would permit the same level of performance. We then applied this validated framework to Coelophysis, demonstrating that it was capable of speeds >6.5 m/s, consistent with data from fossil footprints. These are the first fully 3-D muscle-driven simulations of locomotion in an extinct dinosaur, and pave the way forward for exploring the evolution of bipedality in Archosauria.