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A model is presented which describes the flux-switching processes in a class of batch-fabricated magnetic memory structures. These structures consist of crossed word and bit conductors embedded in a sheet of ferromagnetic material. The model predicts, with fair accuracy, bit-current threshold vs. word current as a function of device geometry. It also makes semiquantitative predictions of flux switched as a function of the write currents. The model is applied to the case of thin ribbon conductors, and the flux efficiency is computed for different device geometries.