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Electromagnetic field analysis methods have been effectively applied to Electrical machinery and devices over the last two decades as reported in the literature [1-10]. However, these methods have been limited to modeling the two-dimensional geometry of the machine or device and employing a single component vector or scalar potential function for the field solution. Electrical machine geometries are essentially three-dimensional and the potential solutions employed must yield all the three vector components of magnetic field and flux-density. Besides, with the increasing attention being focussed on energy efficient designs and reliability of apparatus in service, performance prediction and evaluation of design parameters such as end-leakage fluxes, inductances, time constants, losses, forces, torque etc., must be more accurately done than ever before. This paper reports on the development work done to date on three-dimensional modeling methods and their application to electrical machinery, and highlights some of the problems and opportunities for application of these techniques, for the manufacturing and utility industries. This project was partially funded by the Electric Power Research Institute, Palo Alto, California, under RP1288-1, ``Improvement in Accuracy of Prediction of Electrical Machine Constants.''