Fossil tracks represent the only direct record of behaviour and locomotion of extinct animals. A computer model using finite element analysis (FEA) has been developed to simulate vertebrate track formation in cohesive substrates. This model has been designed for, and successfully run on, high performance computing (HPC) resources. A number of individual studies were carried out using the computer model to simulate both abstract indenters and virtual dinosaur autopodia. In addition to the simulation studies, two fossil tracks were described, including the first report of bird tracks at the Mammoth Site of Hot Springs, South Dakota (USA) and a re-description of a 'dinosaur tail drag' as the trace of a crocodilian. Using the computer model, it has been shown that in a wet, soft mud the indentation of a non-webbed virtual tridactyl foot created a resultant track with features analogous to 'webbing' between digits. This 'webbing' was a function of sediment deformation and subsequent failure in 3D, specific to rheology. Apparent webbing impressions were clearly developed only within a limited range of sediment conditions and pedal geometry. Indenter (pedal) geometry and morphology affect track depth independently of substrate and loading parameters. More complex morphologies interact with the cohesive substrate creating a lower effective load than that applied. In non-cohesive substrates such as sand, this effect is reversed, and it is the more compact morphologies that indent to a lesser degree. Virtual sauropod tracks were modelled, based on published soft tissue reconstructions of autopodia anatomy, and published mass/centre of mass estimates. It was shown that foot morphology and differential loading between fore- and hind- limbs leads to a range of substrates in which only the manus or pes are able to generate tracks. This offers a new mechanism for the formation of manus-only sauropod trackways, previously interpreted as having been made by swimming dinosaurs. A series of tracks were simulated using input data (loads, pedal morphologies) from four different dinosaurs (Brachiosaurus, Tyrannosaurus, Struthiomimus, and Edmontosaurus). The cohesive substrates used displayed a 'Goldilocks' effect, allowing the formation for tracks only for a very limited range of loads for any given foot. In addition, there was a strong bias toward larger animals, both in homogeneous and theoretically heterogeneous substrates. These findings imply that interpretations from track assemblages must consider that only a small proportion of the total fauna present may be recorded as a track assemblage due to substrate properties. The use of FEA to simulate dinosaur track formation has been shown to be successful, and offers a number of advantages over physical modelling including; consistency between experiments, specific control over input variables, rapid undertaking of repeatable experiments, and the ability to view subsurface deformation non-destructively. It is hoped that this work will lead to an increased interest in modelling tracks, and offer a quantitative method for studying fossil tracks.