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A joint program involving the study and practical performance of a foil-flyer electromagnetic accelerator has recently been initiated by Atomic Weapons Establishment, Aldermaston, and Loughborough University. As an initial phase of the work, both 0-D and 2-D numerical models for the foil-flyer accelerator have been developed. The 0-D model, although very crude, is capable of providing an insight into the accelerator phenomena and is currently used for parametric design studies. The 2-D model is based on the well-proven Loughborough filamentary modeling technique and is capable of accurately calculating the 2-D distribution of current, velocity, acceleration, and temperature of the flyer, together with the complete distribution of the magnetic and electric fields generated during a shot. The paper presents the two models and compares typical theoretical predictions with the corresponding experimental results.