This work is directed towards linear and nonlinear three dimensional magnetostatic field analysis and computation in electrical devices. Question regarding the validity and uniqueness of numerical field solutions, obtained on the basis of the curl curl approach, has been resolved through analytical proofs, numerical demonstrations, as well as experimental verifications. A nonlinear three dimensional magnetostatic field formulation is developed using the Newton-Raphson approach in conjunction with the three dimensional finite element method for inclusion of nonlinearities in laminated iron cores under saturated conditions. The developed, formulation was successfully implemented and applied to a practical example with considerable magnetic saturation. A method, for the calculation of saturated device winding inductance, is presented. This method is based on an energy perturbation technique and was successfully applied numerically and verified experimentally. Two methods for the calculation of forces on conductor segments as well as magnetized ferrous parts are developed in conjunction with the three dimensional finite element vector potential method. The proximity effect, resulting from considering small or large solution volumes on the field distribution, and the calculated values of force, is examined. It is demonstrated that a large solution volume, with Dirichlet boundary conditions imposed on the outermost surfaces of the volume considered, yield practically the same result, as when the Neumman boundary conditions were imposed on such surfaces. This result is of a considerable significance, from a practical standpoint, since the imposition of Dirichlet type boundary conditions on the outermost boundaries of the volume considered, results in a fewer number of equations to be solved. This, in turn, results in savings of the total execution time and memory costs required for the solution of large problems of two dimensional, and three dimensional fields by finite elements. It is demonstrated that three dimensional field solutions reduce to the corresponding two dimensional field solutions for problems which are inherently two dimensional in nature due to axial symmetry. This result provides a further verification of the validity of the three dimensional finite element formulation presented in this work. / Ph. D.