A novel mesh-free axisymmetric methodology for the determination of the low-frequency current distribution in foil windings is presented in this paper. The proposed methodology applies equivalent models for the foil winding and the iron core, which are based on the field produced by elementary geometric configurations and boundary conditions derived from Maxwell's equations. Power losses in the windings due to skin effect and proximity effect are calculated with the proposed method and the finite-element method (FEM). The comparison of both results showed excellent agreement. The computational performance is also compared with FEM. It has been found that the proposed method achieves significant improvements in computational times compared with FEM retaining the level of precision required for transformer design purposes.