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In this paper, a new transformer model taking into account magnetic intrinsic anisotropy and air gaps core joints has been proposed. Two special elements have been introduced into the model which are simple to implement in software based on Finite Element Method FEM. Each transversal element (T-element) for air gaps model and each longitudinal element (L-element) for anisotropy is characterized by new B-H relationship. This study has analyzed the influence of these parameters on 2D flux distribution in grain-oriented silicon steel of three-phase transformer core. Based on previous model, an equivalent variable air-gap has been used as T-element and has been implemented on programs using FEM. The proposed model allows localized analysis by extending their capabilities to consider the anisotropy. To develop the nonlinear anisotropic permeability modeling, only the B-H curves in the principal directions (Rolling Direction RD and Transverse Direction TD), available directly from the manufacturers, are required. The results obtained are validated qualitatively by comparison to works using complex anisotropy models and quantitatively by the reproduction of no-load currents of a 10 kVA three limbs three-phase transformer.