A joint programme involving the study and practical performance of a foil-flyer electromagnetic accelerator has recently been initiated by A WE, Aldermaston and Loughborough University. As an initial phase of the work, both O-D and 2-D numerical models for the foil-flyer accelerator have been developed. The O-D model, although very crude, is capable of providing an insight into the accelerator phenomena and currently it is used for parametric design studies. The 2-D model is based on the well-proven Loughborough filamentary modeling technique and is capable of calculating accurately the 2-D distribution of the 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 will present the two models and compare typical theoretical predictions with the corresponding experimental results. Finally, brief comments are made on the proposed way ahead.