A network method is presented for the numerical solution of general three-dimensional electromagnetic field problems. Two physically separate circuit models are derived to represent the electric and magnetic parts of the field. Linkage between the two parts of the network model is through mesh variables. Conventional network techniques are used to define a minimum independent set of mesh variables, for which the linked network is solved. The solution of the simultaneous equations from the network field model, by a preconditioned conjugate gradient algorithm, is described. The main problems that have been found to occur in the use of this algorithm are demonstrated. It is shown how these problems are related to the form of the network model used. Recommendations are made as to how the preconditioned conjugate gradient algorithm can be used most efficiently for the solution of the linked network mesh field equations. The validity and accuracy of the linked network method, for solution of the general three-dimensional electromagnetic field, is demonstrated by a comprehensive comparison of calculated and experimental results for power frequency eddy current problems. Good agreement is shown to be obtained between calculation and experiment. A form of the full three-dimensional linked network model is developed for problems that are periodic along one cartesian coordinate direction (quasi-3D). The validity of this model is confirmed by a comparison of flux density, thrust and normal force calculations with experiment for an axial flux linear motor. Where applicable, the quasi-3D model greatly reduces the cost, in terms of both computer time and storage, of a full three-dimensional field solution.