In order to minimize eddy current losses, the laminated transformer core consists of a large number of very thin ferromagnetic laminations separated from each other by much thinner layers of electrical insulation. As expected, the final solutions for electromagnetic fields in such a heterogeneous region are highly oscillatory, piecewise continuous spatial functions. In order for the approximation of the solution to be valid, the direct application of the finite element method to such a problem requires an extremely dense finite element mesh, i.e., an excessive number of finite elements from the perspective of available computing resources. Therefore, it is necessary to carry out some kind of homogenization of the equations. In the case of an open-type core, the situation is further complicated by the uneven distribution of electromagnetic fields in the core volume. A significant part of the magnetic flux penetrates into the core perpendicular to the surfaces of the laminations, and the eddy currents thus induced have significant values. In order to reduce their amount, the open-type core is usually made of several slimmer parts, i.e. lamination packages, separated from each other by additional layers of electrical insulation. From the point of view of computer simulations, such layers of isolation reduce the speed of convergence, and their homogenization is not possible using standard methods. The specificities of the open-type core can be successfully taken into account using the magnetic vector potential A and the current vector potential T. Accordingly, Galerkin's weak A,T – A-formulation based on the direct application of the finite element method was first derived. In order to significantly reduce the required density of domain discretization, appropriate approximations in the form of uncoupled, mutually independent electromagnetic fields were introduced within each individual finite element. On the basis of the introduced approximations, a modified weak formulation was derived that allows significantly larger dimensions of the finite element, but is valid only locally, within the volume of the observed finite element. However, the homogenization of such a modified formulation gives the Galerkin A,Tx – A-formulation, which is valid globally, within the entire problem domain. As a consequence of the homogenization process, new homogeneous and anisotropic material features are used in the core region. The final A,Tx – A-formulation enables the simultaneous modeling of all eddy currents in the core. Additionally, unlike the initial weak A,T – A-formulation, the homogenized weak A,Tx – A-formulation shows an excellent convergence rate. In addition to the analytical homogenization procedure, a numerical approach to homogenization was developed based on the 2D formulation of the eddy current problem, which takes into account the edge effects of eddy currents, i.e., changes in the direction of eddy currents that occur at the edges of lamin ations. A comparison was made between the simulation based on the A,Tx – A-formulation and the simulation based on the A,φ – A-formulation . A good agreement of the simulation results was obtained, and the simulation based on the A,Tx – A-formulation shows a better convergence rate. Additionally, the developed method was applied to the calculation of losses in a real open-type core for which total losses were previously measured. The simulation results are in good agreement with the results obtained through measurements, which additionally confirms the validity of the developed method.