Boundary-based methods are an alternative to the standard domain-based finite element methods found in most field analysis software. This dissertation examines two boundary-based methods, the Schwarz-Christoffel (S-C) transformation and the boundary element method (BEM), and assesses their feasibility for incorporation into electric machine design tools.;Electric machine design considerations are discussed, and data are given showing that large-scale numerical field analysis software is too slow for rapid iterative design loops. Next, an S-C transformation method coupling S-C maps to analytical field solutions is proposed. Although limited to two-dimensional (2D) problems, this method can quickly narrow a design space without sacrificing machine geometry information. BEM is then discussed, and both 2D and three-dimensional (3D) models for magnetostatic and eddy current problems are presented that are specifically formulated to model electromechanical systems. Simulations using the 2D magnetostatic model closely match data from an electromagnetic actuator operating in its linear range, but those using the 3D model, which incorporates eddy currents, are less accurate. The inaccuracies are found to be likely attributable to the poor performance of the Rao-Wilton-Glisson basis functions at low frequencies.;The thrust in a linear induction motor (LIM) is measured for three different rotor bar materials to test the 2D eddy current BEM model. The model is able to predict thrust-slip curves similar in shape to the measured ones, but the BEM model's curve magnitudes are roughly a factor of two too small. Higher-order basis and testing functions are cited as the likely fix to this inaccuracy.;Boundary- and domain-based field analysis methods are compared in detail with respect to ideal design tool characteristics. Alternative algorithms, including fast solvers and hybrid methods, and parallel processing of solutions are discussed. A hybrid electric machine design optimization scheme is proposed that utilizes the strengths of several of the methods discussed.;The results indicate that boundary-based methods, although not ideal for machine design by themselves, have certain aspects that complement traditional domain-based methods. They therefore merit further study in this context.