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Simple equivalent permeability and reluctance models are obtained for the transformer core joints from the analysis of the magnetic flux. It is shown that the flux variations in the joint zone can be fitted with simple Gaussian expressions suitable for transformer design purposes. These models are derived from 2D and 3D finite element simulations. The magnetic flux distribution in the transformer core joints is studied for wound cores and stacked-lamination cores with step-lap configurations. The models of the study properly account for the effects of core design parameters such as length of air gaps, number of laminations per step and overlap length. The proposed models, which include saturation and anisotropy, are applied to grain-oriented silicon steel (GOSS) and super GOSS. The new models are intended to estimate, right from the design phase, the magnetic flux density, permeability and the reluctance in the joints. The maximum differences between the Gaussian models of this study and finite element simulations are under 6%. The models of this study can be used to improve core designs with the aim of reducing core losses and magnetising current. A comparison of the total losses computed with the model of the study and measurements on a wound core distribution transformer showed differences of about 2.5%.